wanyu/IteraTeR_full_sent huggingface dataset:
Original:   Our real-time operationalization of Strong's model  makes it possible to embed epidemic psychology in any real-time model (e.g., epidemiological and mobility models).
Revised:  Overall, refusal of accepting reality gradually died off as the year went on, while acceptance increasingly took hold. During 2020, as cases surged in waves, so did anger, re-emerging cyclically at each wave. Our real-time operationalization of Strong's model makes it possible to embed epidemic psychology in any real-time model (e.g., epidemiological and mobility models).
Edit intent: meaning-changed
Original:  In  numerical experiments from classification and surrogate modeling, GNvpro not only solves the optimization problem more efficiently but also yields DNNs that generalize better than commonly-used optimization schemes .
Revised:  In numerical experiments from classification and surrogate modeling, segmentation, and classification GNvpro solves the optimization problem more efficiently but also yields DNNs that generalize better than commonly-used optimization schemes .
Edit intent: meaning-changed
Original:  In  numerical experiments from classification and surrogate modeling, GNvpro not only solves the optimization problem more efficiently but also yields DNNs that generalize better than commonly-used optimization schemes .
Revised:  In numerical experiments from classification and surrogate modeling, GNvpro not only solves the optimization problem more efficiently but also yields DNNs that generalize better than commonly-used stochastic gradient descent (SGD) schemes. Also, GNvpro finds solutions that generalize well, and in all but one example better than well-tuned SGD methods, to unseen data points .
Edit intent: meaning-changed
Original:  Ax_{k+1}-b\right\|^2_{2} \leq \left(1 + c_{A}{\|A\|_F^2}\right) \left\|A x_k -b \right\|^2_{2} - 2{\|A\|_F^2} \left\|A^T (Ax _k - b )\right\|^2_{2}.
Revised:  Ax_{k+1}-b\right\|^2_{2} \leq \left(1 + c_{A}{\|A\|_F^2}\right) \left\|A x_k -b \right\|^2_{2} - 2{\|A\|_F^2} \left\|A^T A (x _k - b )\right\|^2_{2}.
Edit intent: meaning-changed
Original:  Ax_{k+1}-b\right\|^2_{2} \leq \left(1 + c_{A}{\|A\|_F^2}\right) \left\|A x_k -b \right\|^2_{2} - 2{\|A\|_F^2} \left\|A^T (Ax _k - b )\right\|^2_{2}.
Revised:  Ax_{k+1}-b\right\|^2_{2} \leq \left(1 + c_{A}{\|A\|_F^2}\right) \left\|A x_k -b \right\|^2_{2} - 2{\|A\|_F^2} \left\|A^T (Ax _k - x )\right\|^2_{2}.
Edit intent: meaning-changed
Original:  This is a curious inequality: when applied to a discretization of a partial differential equation like -\Delta u = f, the last term measures the regularity of the residual u_k - u in a higher Sobolev space than the remaining terms: if u _k - u has large fourth derivatives (i.e. bi-Laplacian \Delta^2), then SGD will dramatically decrease the size of the second derivatives (i. e. \Delta) of u_k - u. For symmetric matrices, this inequality has an extension to higher-order Sobolev spaces.
Revised:  This is a curious inequality: the last term measures the regularity of the residual u_k - u in a higher Sobolev space than the remaining terms: if u _k - u has large fourth derivatives (i.e. bi-Laplacian \Delta^2), then SGD will dramatically decrease the size of the second derivatives (i. e. \Delta) of u_k - u. For symmetric matrices, this inequality has an extension to higher-order Sobolev spaces.
Edit intent: clarity
Original:  This is a curious inequality: when applied to a discretization of a partial differential equation like -\Delta u = f, the last term measures the regularity of the residual u_k - u in a higher Sobolev space than the remaining terms: if u _k - u has large fourth derivatives (i.e. bi-Laplacian \Delta^2), then SGD will dramatically decrease the size of the second derivatives (i. e. \Delta) of u_k - u. For symmetric matrices, this inequality has an extension to higher-order Sobolev spaces.
Revised:  This is a curious inequality: when applied to a discretization of a partial differential equation like -\Delta u = f, the last term has one more matrix applied to the residual u_k - u in a higher Sobolev space than the remaining terms: if u _k - u has large fourth derivatives (i.e. bi-Laplacian \Delta^2), then SGD will dramatically decrease the size of the second derivatives (i. e. \Delta) of u_k - u. For symmetric matrices, this inequality has an extension to higher-order Sobolev spaces.
Edit intent: clarity
Original:  This is a curious inequality: when applied to a discretization of a partial differential equation like -\Delta u = f, the last term measures the regularity of the residual u_k - u in a higher Sobolev space than the remaining terms: if u _k - u has large fourth derivatives (i.e. bi-Laplacian \Delta^2), then SGD will dramatically decrease the size of the second derivatives (i. e. \Delta) of u_k - u. For symmetric matrices, this inequality has an extension to higher-order Sobolev spaces.
Revised:  This is a curious inequality: when applied to a discretization of a partial differential equation like -\Delta u = f, the last term measures the regularity of the residual u_k - u than the remaining terms: if u _k - u has large fourth derivatives (i.e. bi-Laplacian \Delta^2), then SGD will dramatically decrease the size of the second derivatives (i. e. \Delta) of u_k - u. For symmetric matrices, this inequality has an extension to higher-order Sobolev spaces.
Edit intent: clarity
Original:  This is a curious inequality: when applied to a discretization of a partial differential equation like -\Delta u = f, the last term measures the regularity of the residual u_k - u in a higher Sobolev space than the remaining terms: if u _k - u has large fourth derivatives (i.e. bi-Laplacian \Delta^2), then SGD will dramatically decrease the size of the second derivatives (i. e. \Delta) of u_k - u. For symmetric matrices, this inequality has an extension to higher-order Sobolev spaces.
Revised:  This is a curious inequality: when applied to a discretization of a partial differential equation like -\Delta u = f, the last term measures the regularity of the residual u_k - u in a higher Sobolev space than the remaining terms: if x _k - u has large fourth derivatives (i.e. bi-Laplacian \Delta^2), then SGD will dramatically decrease the size of the second derivatives (i. e. \Delta) of u_k - u. For symmetric matrices, this inequality has an extension to higher-order Sobolev spaces.
Edit intent: clarity
Original:  This is a curious inequality: when applied to a discretization of a partial differential equation like -\Delta u = f, the last term measures the regularity of the residual u_k - u in a higher Sobolev space than the remaining terms: if u _k - u has large fourth derivatives (i.e. bi-Laplacian \Delta^2), then SGD will dramatically decrease the size of the second derivatives (i. e. \Delta) of u_k - u. For symmetric matrices, this inequality has an extension to higher-order Sobolev spaces.
Revised:  This is a curious inequality: when applied to a discretization of a partial differential equation like -\Delta u = f, the last term measures the regularity of the residual u_k - u in a higher Sobolev space than the remaining terms: if u _k - x is mainly comprised of large singular vectors, stochastic gradient descent leads to a quick regularization. For symmetric matrices, this inequality has an extension to higher-order Sobolev spaces.
Edit intent: meaning-changed
Original: The layer-ordered heap (LOH) is a novel data structure used in optimal selection on a Cartesian sum, algorithms with the best known runtime for selection on X_1+X_2+\cdots+X_m, and the world's fastest isotope calculator .
Revised: The layer-ordered heap (LOH) is a simple, recently proposed data structure used in optimal selection on a Cartesian sum, algorithms with the best known runtime for selection on X_1+X_2+\cdots+X_m, and the world's fastest isotope calculator .
Edit intent: meaning-changed
Original: The layer-ordered heap (LOH) is a novel data structure used in optimal selection on a Cartesian sum, algorithms with the best known runtime for selection on X_1+X_2+\cdots+X_m, and the world's fastest isotope calculator .
Revised: The layer-ordered heap (LOH) is a novel data structure used in optimal selection on X+Y, thealgorithm with the best known runtime for selection on X_1+X_2+\cdots+X_m, and the world's fastest isotope calculator .
Edit intent: meaning-changed
Original: The layer-ordered heap (LOH) is a novel data structure used in optimal selection on a Cartesian sum, algorithms with the best known runtime for selection on X_1+X_2+\cdots+X_m, and the world's fastest isotope calculator .
Revised: The layer-ordered heap (LOH) is a novel data structure used in optimal selection on a Cartesian sum, algorithms with the best known runtime for selection on X_1+X_2+\cdots+X_m, and the fastest method in practice for computing the most abundant isotope peaks in a chemical compound .
Edit intent: meaning-changed
Original: There remains much uncertainty about the relative effectiveness of different nonpharmaceutical interventions (NPIs) against COVID-19 transmission. Several studies attempt to infer NPI effectiveness with cross-country, data-driven modelling, by linking from NPI implementation dates to the observed timeline of cases and deaths in a country. These models makemany assumptions. Previous work sometimes tests the sensitivity to variations in explicit epidemiological model parameters, but rarely analyses the sensitivity to the assumptions that are made by the choice the of model structure (structural sensitivity analysis). Such analysis would ensure that the inferences made are consistent under plausible alternative assumptions. Without it, NPI effectiveness estimates cannot be used to guide policy.
Revised: There remains much uncertainty about the relative effectiveness of different nonpharmaceutical interventions (NPIs) against COVID-19 influenced by the assumptions our models make? To answer this question, we investigate 2 state-of-the-art NPI effectiveness models and propose 6 variants that make different structural assumptions. In particular, we investigate how well NPI effectiveness estimates cannot be used to guide policy.
Edit intent: coherence
Original:  Without it, NPI effectiveness estimates cannot be used to guide policy. We investigate four model structures similar to a recent state-of-the-art Bayesian hierarchical model. We find that the models differ considerably in the robustness of their NPI effectiveness estimates to changes in epidemiological parameters and the data.
Revised:  Without it, NPI effectiveness estimates generalise to unseen countries, and their sensitivity to unobserved factors. Models that account for noise in disease transmission compare favourably. We further evaluate how robust estimates are to different choices of epidemiological parameters and the data.
Edit intent: meaning-changed
Original:  We find that the models differ considerably in the robustness of their NPI effectiveness estimates to changes in epidemiological parameters and the data. Considering only the models that have good robustness , we find that results and policy-relevant conclusions are remarkably consistent across the structurally different models.
Revised:  We find that the models differ considerably in the robustness of their NPI effectiveness estimates to changes in epidemiological parameters and data. Focusing on models that assume transmission noise , we find that results and policy-relevant conclusions are remarkably consistent across the structurally different models.
Edit intent: meaning-changed
Original:  Focusing on models that assume transmission noise, we find that previously published results are  robust across these choices and across different models . Finally, we mathematically ground the interpretation of NPI effectiveness estimates when certain common assumptions do not hold.
Revised:  Focusing on models that assume transmission noise, we find that previously published results are remarkably robust across these choices and across different models . Finally, we mathematically ground the interpretation of NPI effectiveness estimates when certain common assumptions do not hold.
Edit intent: clarity
Original:  Focusing on models that assume transmission noise, we find that previously published results are  robust across these choices and across different models . Finally, we mathematically ground the interpretation of NPI effectiveness estimates when certain common assumptions do not hold.
Revised:  Focusing on models that assume transmission noise, we find that previously published results are robust across these variables . Finally, we mathematically ground the interpretation of NPI effectiveness estimates when certain common assumptions do not hold.
Edit intent: clarity
Original:  We then propose a mechanism such that the number of users scales as \mathcal{O}(k/(m\alpha^2) + k/m\epsilon\alpha) and further show that it is nearly-optimal under certain regimes. Thus the privacy penalty is \mathcal{O \Theta (m) times smaller compared to the standard mechanisms  .
Revised:  We then propose a mechanism such that the number of users scales as \mathcal{O}(k/(m\alpha^2) + k/m\epsilon\alpha) and hence the privacy penalty is \mathcal{O \Theta (m) times smaller compared to the standard mechanisms .
Edit intent: coherence
Original:  Two classical results drive the entire theory: the Kolmogorov-Cram\'{e The paper develops necessary and sufficient conditions for existence and uniqueness of particular and generic systems . The space of all solutions is characterized as an affine space in the frequency domain , which sheds light on the variety of solution methods considered in the literature .
Revised:  Two classical results drive the entire theory: the Kolmogorov-Cram\'{e The paper develops necessary and sufficient conditions for existence and uniqueness of particular and generic systems and characterizes the space of all solutions is characterized as an affine space in the frequency domain , which sheds light on the variety of solution methods considered in the literature .
Edit intent: coherence
Original:  This motivates regularized solutions with theoretically guaranteed smoothness properties. As an application, the limiting Gaussian likelihood functions of solutions is derived analytically and its properties are studied.
Revised:  This motivates regularized solutions with theoretically guaranteed uniqueness, continuity, and even differentiability properties. Regularization is illustrated in an analysis of the limiting Gaussian likelihood functions of solutions is derived analytically and its properties are studied.
Edit intent: meaning-changed
Original:  The optimal control strategies are categorized as ' suppression' and ' mitigation' strategies and are analyzed in both deterministic and stochastic models. In the stochastic model, vaccination at an uncertain time is taken into account .
Revised:  The optimal control strategies are categorized as ' suppression' and ' mitigation' strategies . We analyze how these strategies change when we incorporate vaccination into the model and find a new optimal `delay-mitigation' strategy .
Edit intent: meaning-changed
Original:  The new technique combines the strengths of both methods, and attains high-order convergence, numerical stability, ease of implementation, and compatibility with the ``fast'' algorithms (such as the Fast Multipole Method or Fast Direct Solvers).
Revised:  The new technique combines the strengths of both methods, and attains high-order convergence, numerical stability, ease of implementation, and compatibility with the "fast" algorithms (such as the Fast Multipole Method or Fast Direct Solvers).
Edit intent: fluency
Original:  Moreover, we prove that our approach, which reduces to an efficiently solvable convex optimization problem, is equivalent to Variational Bayesian inference on the binary connection weights, and we derive rigorous bounds on the posterior marginals.
Revised:  Moreover, we prove that our approach, which reduces to an efficiently solvable convex optimization problem, can be related to Variational Bayesian inference on the binary connection weights, and we derive rigorous bounds on the posterior marginals.
Edit intent: clarity
Original:  This allows us to extend our method to the streaming setting, where continuously updated posteriors allow for optional stopping, and we demonstrate the feasibility of inferring connectivity for networks of up to tens of thousands of neurons online  .
Revised:  This allows us to extend our method to the streaming setting, where continuously updated posteriors allow for optional stopping, and we demonstrate the feasibility of inferring connectivity for networks of up to tens of thousands of neurons online . Finally, we show how our work can be theoretically linked to compressed sensing approaches, and compare results for connectivity inference in different settings .
Edit intent: meaning-changed
Original: We propose and compare methods for the estimation of extreme event probabilities in complex systems governed by PDEs . Our approach is guided by ideas from large deviation theory (LDT) and borrows tools from PDE-constrained optimization. The systems under consideration involve random parameters and we are interested in quantifying the probability that a scalar function of the system state solution is at or above a threshold.
Revised: We propose and compare methods for the estimation of extreme event probabilities in complex systems governed by PDEs that involve random parameters and we are interested in quantifying the probability that a scalar function of the system state solution is at or above a threshold.
Edit intent: clarity
Original:   Our methods first compute parameters that minimize the LDT-rate function over the set of parameters leading to extreme events . These solutions provide asymptotic information about small probability events . We propose a series of methods to refine these estimates, namely methods based on importance sampling and on geometric approximation of the extreme event sets.
Revised:  Our methods first compute parameters that minimize the LDT-rate function over the set of parameters leading to extreme events , using adjoint methods to compute the gradient of this rate function. The minimizers give information about the mechanism of the extreme events as well as estimates of their probability. We then propose a series of methods to refine these estimates, namely methods based on importance sampling and on geometric approximation of the extreme event sets.
Edit intent: meaning-changed
Original:  Adjoint methods are used to compute the derivatives needed to solve the LDT-optimization problem. We present a comparison of the methods for extreme event probability estimation, and find which type of ocean floor elevation change leads to the largest tsunamis on shore.
Revised:  In the context of this example, we present a comparison of the methods for extreme event probability estimation, and find which type of ocean floor elevation change leads to the largest tsunamis on shore.
Edit intent: clarity
Original:  Given that biclique edge-partition, we show how to solve the unweighted Single-Source Shortest Paths and hence All-Pairs Shortest Paths in sublinear time O(n \log n) and time O(n^2 \log n), respectively  .
Revised:  Given that biclique edge-partition, we show how to solve the unweighted Single-Source Shortest Paths and hence All-Pairs Shortest Paths in sublinear time O(n \log n) and time O(n^2 \log n), respectively . Finally we show that Min Dominating Set and related problems have constant integrality gaps on bounded twin-width classes, thereby getting constant approximations on these classes .
Edit intent: meaning-changed
Original:  We specifically investigate whether the vertical spaces of these buildings comprising outdoor corridors, facades and windows receive sufficient photosynthetically active radiation (PAR) for growing food crops and do so at a high resolution.
Revised:  We specifically investigate whether the vertical spaces of these buildings comprising outdoor corridors, fa\c{c and windows receive sufficient photosynthetically active radiation (PAR) for growing food crops and do so at a high resolution.
Edit intent: fluency
Original:  Environmental simulations on the 3D model of the study area indicated that the cumulative daily PAR or Daily Light Integral (DLI) at a location in the building was dependent on its orientation and shape, sun's diurnal and annual motion, weather conditions, and shadowing effects of the building's facades and surrounding buildings.
Revised:  Environmental simulations on the 3D model of the study area indicated that the cumulative daily PAR or Daily Light Integral (DLI) at a location in the building was dependent on its orientation and shape, sun's diurnal and annual motion, weather conditions, and shadowing effects of the building's fa\c{c and surrounding buildings.
Edit intent: fluency
Original:  Besides a direct k-pass implementation of classical spanner constructions ,\lfloor\rfloor the state of the art amounts to a O(\log k)-pass algorithm of Ahn, Guha and McGregor'12, and a 2-pass algorithm of Kapralov and Woodruff'14.
Revised:  Besides a direct k-pass implementation of classical spanner constructions (recently improved to\lfloor\rfloor the state of the art amounts to a O(\log k)-pass algorithm of Ahn, Guha and McGregor'12, and a 2-pass algorithm of Kapralov and Woodruff'14.
Edit intent: meaning-changed
Original:  Besides a direct k-pass implementation of classical spanner constructions ,\lfloor\rfloor the state of the art amounts to a O(\log k)-pass algorithm of Ahn, Guha and McGregor'12, and a 2-pass algorithm of Kapralov and Woodruff'14.
Revised:  Besides a direct k-pass implementation of classical spanner constructions ,\lfloor\frac k2\rfloor the state of the art amounts to a O(\log k)-pass algorithm of Ahn, Guha and McGregor'12, and a 2-pass algorithm of Kapralov and Woodruff'14.
Edit intent: meaning-changed
Original:  Besides a direct k-pass implementation of classical spanner constructions ,\lfloor\rfloor the state of the art amounts to a O(\log k)-pass algorithm of Ahn, Guha and McGregor'12, and a 2-pass algorithm of Kapralov and Woodruff'14.
Revised:  Besides a direct k-pass implementation of classical spanner constructions ,\lfloor\rfloor+1-passes by Fernandez, Woodruff and Yasuda'20) the state of the art amounts to a O(\log k)-pass algorithm of Ahn, Guha and McGregor'12, and a 2-pass algorithm of Kapralov and Woodruff'14.
Edit intent: meaning-changed
Original:  We give the first {\em single pass} sketching algorithm for constructing graph spanners: we show how to obtain a O(n^{ \frac{2 \frac23 })-spanner using O(n) space, and in general a O(n^{ \frac{2 \frac23 (1-\alpha)})-spanner using O(n^{1+\alpha}) space for every \alpha\in [0, 1], a tradeoff that we think may be close optimal.
Revised:  We give the first {\em single pass} sketching algorithm for constructing graph spanners: we show how to obtain a O(n^{ \frac23 })-spanner using O(n) space, and in general a O(n^{ \frac{2 \frac23 (1-\alpha)})-spanner using O(n^{1+\alpha}) space for every \alpha\in [0, 1], a tradeoff that we think may be close optimal.
Edit intent: fluency
Original:  We give the first {\em single pass} sketching algorithm for constructing graph spanners: we show how to obtain a O(n^{ \frac{2 \frac23 })-spanner using O(n) space, and in general a O(n^{ \frac{2 \frac23 (1-\alpha)})-spanner using O(n^{1+\alpha}) space for every \alpha\in [0, 1], a tradeoff that we think may be close optimal.
Revised:  We give the first {\em single pass} sketching algorithm for constructing graph spanners: we show how to obtain a O(n^{ \frac{2 \frac23 })-spanner using O(n) space, and in general a O(n^{ \frac23 (1-\alpha)})-spanner using O(n^{1+\alpha}) space for every \alpha\in [0, 1], a tradeoff that we think may be close optimal.
Edit intent: fluency