wanyu/IteraTeR_full_sent huggingface dataset:
Original:  In this paper, we propose a unified way to analyze the convergence via directly studying the error of the algorithm and using the stability of the time integrator. Our analysis works for all^+ with \sigma(A) being the spectrum of A\inC^{m\times m}.
Revised:  In this paper, we propose a unified convergence analysis for the algorithm applied to u'+Au=f, where \sigma(A)\subset\mathbb{C^+ with \sigma(A) being the spectrum of A\inC^{m\times m}.
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Original:  For any } one-step time-integrators and two exemplary classes of two-step time-integrators: the parameterized Numerov methodsand the parameterized two-stage hybrid methods. The main conclusion is that the global error satisfies \|{\textbf{err}^{k+1}\|_{{\mathbf W},
Revised:  For any } one-step }^{k+1}\|_{{\mathbf W},
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Original:  2}\leq \alpha{1-\alpha}\|{err}^{k}\|_{{\mathbf W}, 2} provided that the time-integrator } (z), we prove that the decay rate of the global error is bounded by \alpha/(1-\alpha), provided the method } is stable, where k is the iteration index and for any vector v the norm \|v\|_{{\mathbf W, 2} is defined by \|v\|_{{\mathbf W}, 2}=\|{\mathbf W}v\|_2 with }%DIFDELCMD < {%%% \mathbf W being a matrix depending on the space discretization matrix only.
Revised:  2}\leq \alpha{1-\alpha}\|{err}^{k}\|_{{\mathbf W}, 2} provided that the time-integrator } method (such as the Runge-Kutta methods) with stability function \mathcal{R(z), we prove that the decay rate of the global error is bounded by \alpha/(1-\alpha), provided the method } is stable, where k is the iteration index and for any vector v the norm \|v\|_{{\mathbf W, 2} is defined by \|v\|_{{\mathbf W}, 2}=\|{\mathbf W}v\|_2 with }%DIFDELCMD < {%%% \mathbf W being a matrix depending on the space discretization matrix only.
Edit intent: meaning-changed
Original:  2}\leq \alpha{1-\alpha}\|{err}^{k}\|_{{\mathbf W}, 2} provided that the time-integrator } (z), we prove that the decay rate of the global error is bounded by \alpha/(1-\alpha), provided the method } is stable, where k is the iteration index and for any vector v the norm \|v\|_{{\mathbf W, 2} is defined by \|v\|_{{\mathbf W}, 2}=\|{\mathbf W}v\|_2 with }%DIFDELCMD < {%%% \mathbf W being a matrix depending on the space discretization matrix only.
Revised:  2}\leq \alpha{1-\alpha}\|{err}^{k}\|_{{\mathbf W}, 2} provided that the time-integrator } (z), we prove that the decay rate of the global error is bounded by \alpha/(1-\alpha), provided the method } is stable, , 2} is defined by \|v\|_{{\mathbf W}, 2}=\|{\mathbf W}v\|_2 with }%DIFDELCMD < {%%% \mathbf W being a matrix depending on the space discretization matrix only.
Edit intent: coherence
Original:  2}\leq \alpha{1-\alpha}\|{err}^{k}\|_{{\mathbf W}, 2} provided that the time-integrator } (z), we prove that the decay rate of the global error is bounded by \alpha/(1-\alpha), provided the method } is stable, where k is the iteration index and for any vector v the norm \|v\|_{{\mathbf W, 2} is defined by \|v\|_{{\mathbf W}, 2}=\|{\mathbf W}v\|_2 with }%DIFDELCMD < {%%% \mathbf W being a matrix depending on the space discretization matrix only.
Revised:  2}\leq \alpha{1-\alpha}\|{err}^{k}\|_{{\mathbf W}, 2} provided that the time-integrator } (z), we prove that the decay rate of the global error is bounded by \alpha/(1-\alpha), provided the method } is stable, where k is the iteration index and for any vector v the norm \|v\|_{{\mathbf W, 2} is defined by \|v\|_{{\mathbf W}, 2}=\|{\mathbf W}v\|_2 with }%DIFDELCMD < {%%% being a matrix depending on the space discretization matrix only.
Edit intent: coherence
Original:  2}\leq \alpha{1-\alpha}\|{err}^{k}\|_{{\mathbf W}, 2} provided that the time-integrator } (z), we prove that the decay rate of the global error is bounded by \alpha/(1-\alpha), provided the method } is stable, where k is the iteration index and for any vector v the norm \|v\|_{{\mathbf W, 2} is defined by \|v\|_{{\mathbf W}, 2}=\|{\mathbf W}v\|_2 with }%DIFDELCMD < {%%% \mathbf W being a matrix depending on the space discretization matrix only. Even though we focus on wave equations in this paper, the proposed argument is directly applicable to other evolution problems|\mathcal{R}(\Delta t\lambda)|}\leq1\geq1  .
Revised:  2}\leq \alpha{1-\alpha}\|{err}^{k}\|_{{\mathbf W}, 2} provided that the time-integrator } (z), we prove that the decay rate of the global error is bounded by \alpha/(1-\alpha), provided the method } is stable, where k is the iteration index and for any vector v the norm \|v\|_{{\mathbf W, 2} is defined by \|v\|_{{\mathbf W}, 2}=\|{\mathbf W}v\|_2 with }%DIFDELCMD < {%%% \mathbf W i.e., \max_{\lambda\in\sigma(A)|\mathcal{R}(\Delta t\lambda)|}\leq1\geq1 .
Edit intent: meaning-changed
Original:  Even though we focus on wave equations in this paper, the proposed argument is directly applicable to other evolution problems|\mathcal{R}(\Delta t\lambda)|}\leq1\geq1  .
Revised:  Even though we focus on wave equations in this paper, the proposed argument is directly applicable to other evolution problems|\mathcal{R}(\Delta t\lambda)|}\leq1. For any linear multistep method, such a bound becomes c\alpha/(1-c\alpha), where c\geq1 .
Edit intent: meaning-changed
Original:  Even though we focus on wave equations in this paper, the proposed argument is directly applicable to other evolution problems|\mathcal{R}(\Delta t\lambda)|}\leq1\geq1  .
Revised:  Even though we focus on wave equations in this paper, the proposed argument is directly applicable to other evolution problems|\mathcal{R}(\Delta t\lambda)|}\leq1\geq1 is a constant specified by the multistep method itself. Our proof only relies on the stability of the time-integrator and the estimate is independent of the step size \Delta t and the spectrum \sigma(A) .
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Original:  This not only can help to interpret these measures , but also the computational advantage is enormous when analyzing real-world networks, often characterized by large and sparse adjacency matrices: instead of looping over nodes, one can rely on very efficient and fast matrix operations(e.g., multiplication) .
Revised:  This can help to interpret these measures , but also the computational advantage is enormous when analyzing real-world networks, often characterized by large and sparse adjacency matrices: instead of looping over nodes, one can rely on very efficient and fast matrix operations(e.g., multiplication) .
Edit intent: clarity
Original:  We propose a novel fine-tuning algorithm, %DIFDELCMD < \ours%%%  , that consists of a relaxing stage and a curriculum learning stage to enable transfer learning across homotopy classes.
Revised:  We propose a novel fine-tuning algorithm, %DIFDELCMD < \ours%%% Ease-In-Ease-Out fine-tuning , that consists of a relaxing stage and a curriculum learning stage to enable transfer learning across homotopy classes.
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Original:  Finally, we evaluate our approach on several robotics-inspired simulated environments and empirically verify that the %DIFDELCMD < \ours%%% \ method can successfully fine-tune in a sample-efficient way compared to existing baselines.
Revised:  Finally, we evaluate our approach on several robotics-inspired simulated environments and empirically verify that the %DIFDELCMD < \ours%%% Ease-In-Ease-Out fine-tuning method can successfully fine-tune in a sample-efficient way compared to existing baselines.
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Original: Advances in quantum information processing compel us to explore learning from quantum data . We consider a classical-quantum learning problem in which the samples are quantum states with classical labels and the predictors are quantum measurements .
Revised: Advances in quantum information processing compel us to explore learning from quantum data , in particular quantum state classification which has applications, among others, in classifying the separability of quantum states. In this learning model, there are n quantum states with classical labels and the predictors are quantum measurements .
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Original:  We consider a classical-quantum learning problem in which the samples are quantum states with classical labels and the predictors are quantum measurements . To study this problem , we introduce a quantum counterpart of PAC framework .
Revised:  We consider a classical-quantum learning problem in which the samples are quantum states with classical labels and the predictors are quantum measurements that when applied to the next unseen quantum state predict its classical label. By integrating learning theory with quantum information , we introduce a quantum counterpart of PAC framework .
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Original:  We argue that the major difficulties arising from the quantum nature of the problem are the compatibility of the measurements and the no-cloning principle . With that in mind, we establish bounds on the quantum sample complexity for a family of quantum concept classes called concentrated measurements . Using a quantum Fourier expansion on qubits, we propose a quantum low-degree learning algorithm which is a quantum counterpart of (Linial et al., 1993) .
Revised:  We argue that the major difficulties arising from the quantum nature of the problem are the compatibility of the measurements and the no-cloning principle -- prohibiting sample reuse. Then, after introducing a Fourier expansion through Pauli's operators, we study learning with respect to an infinite class of quantum measurements whose operator's Fourier spectrum is concentrated on low degree terms. We propose a quantum low-degree learning algorithm which is a quantum counterpart of (Linial et al., 1993) .
Edit intent: clarity
Original:  With that in mind, we establish bounds on the quantum sample complexity for a family of quantum concept classes called concentrated measurements . Using a quantum Fourier expansion on qubits, we propose a quantum low-degree learning algorithm which is a quantum counterpart of (Linial et al., 1993) .
Revised:  With that in mind, we establish bounds on the quantum sample complexity for a family of quantum concept classes called concentrated measurements . Using a quantum Fourier expansion on qubits, we propose a quantum learning algorithm and show that the quantum sample complexity depends on the ``compatibility structure" of such measurement classes -- the more compatible the class is, the lower the quantum sample complexity will be. We further introduce k-junta measurements as a special class of low-depth quantum circuits whose Fourier spectrum is concentrated on low degrees .
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Original: Determinantal point processes (DPPs) are widely popular probabilistic models used in machine learning to capture diversity in random subsets of items. While traditional DPPs are defined by a symmetric kernel matrix, recent work has shown a significant increase in the modeling power and applicability of models defined by nonsymmetric kernels, where the model can capture interactions that go beyond diversity. We study the problem of maximum a posteriori (MAP ) inference for determinantal point processes defined by a nonsymmetric positive semidefinite matrix (NDPPs), where the goal is to find the maximum k \times k principal minor of the kernel matrix L . We obtain the first multiplicative approximation guarantee for this problem using local search, a method that has been previously applied to symmetric DPPs.
Revised: We show a connection between sampling and optimization on discrete domains. For a family of distributions \mu defined on size k subsets of a ground set of elements that is closed under external fields, we show that rapid mixing of natural local random walks implies the existence of simple approximation algorithms to find \max \mu(\cdot). More precisely we show that if (multi-step) down-up random walks have spectral gap at least inverse polynomially large in k, then (multi-step) local search can find \max \mu(\cdot) within a factor of k^{O(k) principal minor of the kernel matrix L . We obtain the first multiplicative approximation guarantee for this problem using local search, a method that has been previously applied to symmetric DPPs.
Edit intent: meaning-changed
Original:  We study the problem of maximum a posteriori (MAP ) inference for determinantal point processes defined by a nonsymmetric positive semidefinite matrix (NDPPs), where the goal is to find the maximum k \times k principal minor of the kernel matrix L . We obtain the first multiplicative approximation guarantee for this problem using local search, a method that has been previously applied to symmetric DPPs. Our approximation factor of k^{O(k) .
Revised:  We study the problem of maximum a posteriori (MAP ) inference for determinantal point processes defined by a nonsymmetric positive semidefinite matrix (NDPPs), where the goal is to find the maximum k \times k principal minor of a square (not-necessarily-symmetric) matrix L with L+L^\intercal\succeq 0. We establish the connection between sampling and optimization by showing that an exchange inequality, a concept rooted in discrete convex analysis, can be derived from fast mixing of local random walks. We further connect exchange inequalities with composable core-sets for optimization, generalizing recent results on composable core-sets for DPP maximization to arbitrary distributions that satisfy either the strongly Rayleigh property or that have a log-concave generating polynomial .
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Original: Models of asexually reproducing populations in varying environments have provided insights into the diversity of adaptive strategies, revealed deep analogies with information theory and stochastic thermodynamics, and inspired quantitative methods to analyze single-cell experiments.
Revised: The long-term growth rate of populations in varying environments have provided insights into the diversity of adaptive strategies, revealed deep analogies with information theory and stochastic thermodynamics, and inspired quantitative methods to analyze single-cell experiments.
Edit intent: clarity
Original: Models of asexually reproducing populations in varying environments have provided insights into the diversity of adaptive strategies, revealed deep analogies with information theory and stochastic thermodynamics, and inspired quantitative methods to analyze single-cell experiments. Here we show how these models can be generalized to sexually reproducing populations. The resulting framework is applied to two fundamental questions. First, what are the conditions under which sexual reproduction is advantageous over asexual reproduction?
Revised: Models of asexually reproducing populations in varying environments quantifies the evolutionary value of processing the information that biological individuals inherit from their ancestors and acquire from their environment. Previous models were limited to asexual reproduction with inherited information coming from a single parent with no recombination. We present a general extension to sexual reproduction and an analytical solution for a particular but important case, the infinitesimal model of quantitative genetics which assumes traits to be normally distributed. We study with this model the conditions under which sexual reproduction is advantageous over asexual reproduction?
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Original:  First, what are the conditions under which sexual reproduction is advantageous over asexual reproduction? Second, what are the conditions under which sexual dimorphism, the presence of two phenotypically distinct sexes , is advantageous?
Revised:  First, what are the conditions under which sexual reproduction is advantageous and can evolve in the context of autocorrelated or directionally varying environments, mutational biases, spatial heterogeneities and phenotypic plasticity. Our results generalize and unify previous analyses. We also examine the proposal made by Geodakyan that the presence of two phenotypically distinct sexes , is advantageous?
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Original:  Second, what are the conditions under which sexual dimorphism, the presence of two phenotypically distinct sexes , is advantageous? We study these questions from the two standpoints of optimal information processing and evolvability. Our analysis provides a new perspective on long-standing problems as well as fresh insights into unexamined questions. More generally , it opens the door to novel interdisciplinary approaches to a central problem of evolutionary biology, the role of sex in adaptation .
Revised:  Second, what are the conditions under which sexual dimorphism, the presence of two phenotypically distinct sexes permits an optimal adaptation to varying environments. We verify that conditions exists where sexual dimorphism is adaptive but find that its evolutionary value does not generally compensate for the two-fold cost of males .
Edit intent: coherence
Original: The ongoing COVID-19 vaccination campaign has so far targeted a less than 2 \% of the world population, and even in countries where the campaign has started many citizens will not receive their doses for many months.
Revised: The ongoing COVID-19 vaccination campaign has so far targeted less than 3 \% of the world population, and even in countries where the campaign has started many citizens will not receive their doses for many months.
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Original:  By February 6 , we found 22 listings offering a COVID-19 vaccine . Three listings offer the Pfizer/BioNTech vaccine, one listing the AstraZeneca/Oxford vaccine, and three listings a fabricated proof of vaccination against COVID-19.
Revised:  By February 6 , we found 22 listings offering a COVID-19 vaccine , seven of which offering officially approved vaccines. The number of currently active listings is 11, including one listing selling the Pfizer/BioNTech vaccine, one listing the AstraZeneca/Oxford vaccine, and three listings a fabricated proof of vaccination against COVID-19.
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Original:  Three listings offer the Pfizer/BioNTech vaccine, one listing the AstraZeneca/Oxford vaccine, and three listings a fabricated proof of vaccination against COVID-19. Several listings appeared before the summer of 2020, and can be deemed as scams .
Revised:  Three listings offer the Pfizer/BioNTech vaccine, one listing the AstraZeneca/Oxford vaccine, and 9 listings selling vaccines of unspecified type .
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Original:  We designed and implemented a randomized field experiment based on detailed patient health activities (e.g., steps, exercises, sleep, food intake) and blood glucose values from 1,070 diabetes patients over several months.
Revised:  We designed a randomized field experiment based on detailed patient health activities (e.g., steps, exercises, sleep, food intake) and blood glucose values from 1,070 diabetes patients over several months.
Edit intent: clarity
Original:  We designed and implemented a randomized field experiment based on detailed patient health activities (e.g., steps, exercises, sleep, food intake) and blood glucose values from 1,070 diabetes patients over several months.
Revised:  We designed and implemented a randomized field experiment based on detailed patient health activities (e.g., exercises, sleep, food intake) and blood glucose values from 1,070 diabetes patients over several months.
Edit intent: clarity
Original:  Our main findings show that the adoption of the mHealth app leads to an improvement in  both short term metrics ( such as reduction in patients' blood glucose and glycated hemoglobin levels) and longer-term metrics ( such as hospital visits , and medical expenses).
Revised:  We find the adoption of the mHealth app leads to an improvement in both short term metrics ( such as reduction in patients' blood glucose and glycated hemoglobin levels) and longer-term metrics ( such as hospital visits , and medical expenses).
Edit intent: coherence
Original:  Our main findings show that the adoption of the mHealth app leads to an improvement in  both short term metrics ( such as reduction in patients' blood glucose and glycated hemoglobin levels) and longer-term metrics ( such as hospital visits , and medical expenses).
Revised:  Our main findings show that the adoption of the mHealth app leads to an improvement in health behavior, which leads to both short term metrics ( such as reduction in patients' blood glucose and glycated hemoglobin levels) and longer-term metrics ( such as hospital visits , and medical expenses).
Edit intent: meaning-changed
Original:  Our main findings show that the adoption of the mHealth app leads to an improvement in  both short term metrics ( such as reduction in patients' blood glucose and glycated hemoglobin levels) and longer-term metrics ( such as hospital visits , and medical expenses).
Revised:  Our main findings show that the adoption of the mHealth app leads to an improvement in both short term metrics ( reduction in patients' blood glucose and glycated hemoglobin levels) and longer-term metrics ( such as hospital visits , and medical expenses).
Edit intent: fluency
Original:  Our main findings show that the adoption of the mHealth app leads to an improvement in  both short term metrics ( such as reduction in patients' blood glucose and glycated hemoglobin levels) and longer-term metrics ( such as hospital visits , and medical expenses).
Revised:  Our main findings show that the adoption of the mHealth app leads to an improvement in both short term metrics ( such as reduction in patients' blood glucose and glycated hemoglobin levels) and longer-term metrics ( hospital visits and medical expenses).
Edit intent: fluency
Original:  PC enabled version of the same app demonstrates that the mobile has a stronger effect than PCs in helping patients make  behavioral modifications with respect to diet, exercise and life style, which ultimately leads to an improvement in their healthcare outcomes.
Revised:  PC version of the same app demonstrates that the mobile has a stronger effect than PCs in helping patients make behavioral modifications with respect to diet, exercise and life style, which ultimately leads to an improvement in their healthcare outcomes.
Edit intent: clarity
Original:  PC enabled version of the same app demonstrates that the mobile has a stronger effect than PCs in helping patients make  behavioral modifications with respect to diet, exercise and life style, which ultimately leads to an improvement in their healthcare outcomes.
Revised:  PC enabled version of the same app demonstrates that mobile has a stronger effect than PCs in helping patients make behavioral modifications with respect to diet, exercise and life style, which ultimately leads to an improvement in their healthcare outcomes.
Edit intent: clarity
Original:  PC enabled version of the same app demonstrates that the mobile has a stronger effect than PCs in helping patients make  behavioral modifications with respect to diet, exercise and life style, which ultimately leads to an improvement in their healthcare outcomes.
Revised:  PC enabled version of the same app demonstrates that the mobile has a stronger effect than PC in helping patients make behavioral modifications with respect to diet, exercise and life style, which ultimately leads to an improvement in their healthcare outcomes.
Edit intent: fluency
Original:  PC enabled version of the same app demonstrates that the mobile has a stronger effect than PCs in helping patients make  behavioral modifications with respect to diet, exercise and life style, which ultimately leads to an improvement in their healthcare outcomes.
Revised:  PC enabled version of the same app demonstrates that the mobile has a stronger effect than PCs in helping patients make these behavioral modifications with respect to diet, exercise and life style, which ultimately leads to an improvement in their healthcare outcomes.
Edit intent: clarity