wanyu/IteraTeR_full_sent huggingface dataset:
Original:  (a) no randomised  algorithm can compute a NN correct to K digits with probability greater than 1/2, (b) there exists a deterministic  algorithm that computes a NN with K-1 correct digits, but any such (even randomised) algorithm needs arbitrarily many training data, (c) there exists a deterministic  algorithm that computes a NN with K-2 correct digits using no more than L training samples.
Revised:  (a) no randomised training algorithm can compute a NN correct to K digits with probability greater than 1/2, (b) there exists a deterministic algorithm that computes a NN with K-1 correct digits, but any such (even randomised) algorithm needs arbitrarily many training data, (c) there exists a deterministic algorithm that computes a NN with K-2 correct digits using no more than L training samples.
Edit intent: fluency
Original:  (a) no randomised  algorithm can compute a NN correct to K digits with probability greater than 1/2, (b) there exists a deterministic  algorithm that computes a NN with K-1 correct digits, but any such (even randomised) algorithm needs arbitrarily many training data, (c) there exists a deterministic  algorithm that computes a NN with K-2 correct digits using no more than L training samples.
Revised:  (a) no randomised algorithm can compute a NN correct to K digits with probability greater than 1/2, (b) there exists a deterministic training algorithm that computes a NN with K-1 correct digits, but any such (even randomised) algorithm needs arbitrarily many training data, (c) there exists a deterministic algorithm that computes a NN with K-2 correct digits using no more than L training samples.
Edit intent: fluency
Original:  (a) no randomised  algorithm can compute a NN correct to K digits with probability greater than 1/2, (b) there exists a deterministic  algorithm that computes a NN with K-1 correct digits, but any such (even randomised) algorithm needs arbitrarily many training data, (c) there exists a deterministic  algorithm that computes a NN with K-2 correct digits using no more than L training samples.
Revised:  (a) no randomised algorithm can compute a NN correct to K digits with probability greater than 1/2, (b) there exists a deterministic algorithm that computes a NN with K-1 correct digits, but any such (even randomised) algorithm needs arbitrarily many training data, (c) there exists a deterministic training algorithm that computes a NN with K-2 correct digits using no more than L training samples.
Edit intent: fluency
Original:  Moreover, we prove that only O(|\log(\epsilon)|) layers are needed for an \epsilon accurate solution to the inverse problem (exponential convergence), and that the inner dimensions in the layers do not exceed the dimension of the inverse problem.
Revised:  Moreover, we prove that only O(|\log(\epsilon)|) layers are needed for an \epsilon -accurate solution to the inverse problem (exponential convergence), and that the inner dimensions in the layers do not exceed the dimension of the inverse problem.
Edit intent: fluency
Original:  Moreover, we prove that only O(|\log(\epsilon)|) layers are needed for an \epsilon accurate solution to the inverse problem (exponential convergence), and that the inner dimensions in the layers do not exceed the dimension of the inverse problem. Thus, FIRENETs are computationally very efficient .
Revised:  Moreover, we prove that only O(|\log(\epsilon)|) layers are needed for an \epsilon accurate solution to the inverse problem .
Edit intent: coherence
Original:  Moreover in a safety critical domain it is essential to know what our agent does and does not know, for this we also quantity the model uncertainty associated with each patient state and action, and propose a general framework for uncertainty aware, interpretable treatment policies.
Revised:  Moreover in a safety critical domain it is essential to know what our agent does and does not know, for this we also quantify the model uncertainty associated with each patient state and action, and propose a general framework for uncertainty aware, interpretable treatment policies.
Edit intent: coherence
Original: Sepsis is the leading cause of mortality in the ICU, responsible for 6\% of all hospitalizations and 35\% of all in-hospital deaths in USA. However, there is no universally agreed upon strategy for vasopressor and fluid administration. It has also been observed that different patients respond differently to treatment, highlighting the need for individualized treatment. Vasopressors and fluids are administrated with specific effects to cardiovascular physiology in mind and medical researchhas suggested that physiologic, hemodynamically guided, approaches to treatment. Thus we propose a novel approach, exploiting and unifying complementary strengths of Mathematical Modelling, Deep Learning, Reinforcement Learning and Uncertainty Quantification, to learn individualized, safe, and uncertainty aware treatment strategies.
Revised: Sepsis is a potentially life threatening inflammatory response to infection or severe tissue damage. It has a highly variable clinical course, requiring constant monitoring of the patient's state to guide the management of intravenous fluids and vasopressors, among other interventions. Despite decades of research, there's still debate among experts on optimal treatment. Here, we combine for the first time, distributional deep reinforcement learning with mechanistic physiological models to find personalized sepsis treatment strategies.
Edit intent: coherence
Original:  We first infer patient-specific, dynamic cardiovascular states using a novel physiology-driven recurrent neural network trained in an unsupervised manner. This information, along with a learned low dimensional representation of the patient's lab history and observable data, is then used to derive value distributions using Batch Distributional Reinforcement Learning. Moreoverin a safety critical domain it is essential to know what our agent does and does not know, for this we also quantify the model uncertainty associated with each patient state and action, and propose a general framework for uncertainty aware , interpretable treatment policies.
Revised:  We first infer patient-specific, dynamic cardiovascular states using a novel physiology-driven recurrent autoencoder, and quantifies the uncertainty of its own results. Moreover, we introduce a framework for uncertainty aware , interpretable treatment policies.
Edit intent: clarity
Original:  Moreoverin a safety critical domain it is essential to know what our agent does and does not know, for this we also quantify the model uncertainty associated with each patient state and action, and propose a general framework for uncertainty aware , interpretable treatment policies. This framework can be tweaked easily, to reflect a clinician's own confidence of the framework, and can be easily modified to factor in human expert opinion, whenever it's accessible. Using representative patients and a validation cohort, we show that our method has learned physiologically interpretable generalizable policies .
Revised:  Moreoverin a safety critical domain it is essential to know what our agent does and does not know, for this we also quantify the model uncertainty associated with each patient state and action, and propose a general framework for uncertainty aware decision support with humans in the loop. We show that our method has learned physiologically interpretable generalizable policies .
Edit intent: clarity
Original:  Numerical examples show the robustness of the method and that it converges at order one in energy norm similarly to the usual Lagrange P2-P1 mixed element. Also, the robustness of the method with respect to the incompressible limit \nu%DIFDELCMD < } \to %%% 0.5 is proved numerically .
Revised:  Numerical examples show the robustness of the method \nu%DIFDELCMD < } \to %%% 0.5 is proved numerically .
Edit intent: coherence
Original:  Also, the robustness of the method with respect to the incompressible limit \nu%DIFDELCMD < } \to %%% 0.5 is proved numerically .
Revised:  Also, the robustness of the method with respect to the incompressible limit \nu%DIFDELCMD < } \to %%% for both static and dynamic computations in two and three dimensions .
Edit intent: meaning-changed
Original:  In the fully discrete scheme, a Crank-Nicolson scheme is adopted for the approximation of the temporal derivatives of displacement and stress . Error estimates of the two schemes, as well as an unconditional stability result for the fully discrete scheme, are derived.
Revised:  In the fully discrete scheme, a Crank-Nicolson scheme is adopted for the approximation of the temporal derivatives of stress and velocity variables . Error estimates of the two schemes, as well as an unconditional stability result for the fully discrete scheme, are derived.
Edit intent: clarity
Original:  In the fully discrete scheme, a Crank-Nicolson scheme is adopted for the approximation of the temporal derivatives of displacement and stress . Error estimates of the two schemes, as well as an unconditional stability result for the fully discrete scheme, are derived.
Revised:  In the fully discrete scheme, a Crank-Nicolson scheme is adopted for the approximation of the temporal derivatives of displacement and stress . Error estimates of the semi-discrete and fully discrete schemes, as well as an unconditional stability result for the fully discrete scheme, are derived.
Edit intent: meaning-changed
Original:  We present our predictions for three countries with quite distinct types of disease progression, namely: (i) India which has had a smooth rise followed by an equally smooth fall-off in the number of active cases , (ii) Italy, which has witnessed multiple peaks in the number of active cases, and has also witnessed multiple "phases" of the pandemic , and (iii) the USA which has erratic recovery data .
Revised:  We present our predictions for countries with three quite distinct types of disease progression, namely: (i) India which has had a smooth rise followed by an equally smooth fall-off in the number of active cases , (ii) Italy, which has witnessed multiple peaks in the number of active cases, and has also witnessed multiple "phases" of the pandemic , and (iii) the USA which has erratic recovery data .
Edit intent: fluency
Original:  We present our predictions for three countries with quite distinct types of disease progression, namely: (i) India which has had a smooth rise followed by an equally smooth fall-off in the number of active cases , (ii) Italy, which has witnessed multiple peaks in the number of active cases, and has also witnessed multiple "phases" of the pandemic , and (iii) the USA which has erratic recovery data .
Revised:  We present our predictions for three countries with quite distinct types of disease progression, namely: (i) countries where nearly all of population still remains outside the reach of the pandemic , (ii) Italy, which has witnessed multiple peaks in the number of active cases, and has also witnessed multiple "phases" of the pandemic , and (iii) the USA which has erratic recovery data .
Edit intent: meaning-changed
Original:  We present our predictions for three countries with quite distinct types of disease progression, namely: (i) India which has had a smooth rise followed by an equally smooth fall-off in the number of active cases , (ii) Italy, which has witnessed multiple peaks in the number of active cases, and has also witnessed multiple "phases" of the pandemic , and (iii) the USA which has erratic recovery data .
Revised:  We present our predictions for three countries with quite distinct types of disease progression, namely: (i) India which has had a smooth rise followed by an equally smooth fall-off in the number of active cases , (ii) countries where a reasonable fraction of population is both within and outside the reach , and (iii) the USA which has erratic recovery data .
Edit intent: meaning-changed
Original:  We present our predictions for three countries with quite distinct types of disease progression, namely: (i) India which has had a smooth rise followed by an equally smooth fall-off in the number of active cases , (ii) Italy, which has witnessed multiple peaks in the number of active cases, and has also witnessed multiple "phases" of the pandemic , and (iii) the USA which has erratic recovery data .
Revised:  We present our predictions for three countries with quite distinct types of disease progression, namely: (i) India which has had a smooth rise followed by an equally smooth fall-off in the number of active cases , (ii) Italy, which has witnessed multiple peaks in the number of active cases, and has also witnessed multiple "phases" of the pandemic , and (iii) countries where nearly all of population s within the reach of the pandemic .
Edit intent: meaning-changed
Original: The textbook Newton's iteration is practically inapplicable on nonisolated solutions of unregularized nonlinear systems . With a simple modification, a version of Newton's iteration regains its local quadratic convergence to nonisolated zeros of smooth mappings assuming the solutions are semiregular as properly defined regardless of whether the system is square, underdetermined or overdetermined  .
Revised: The textbook Newton's iteration is practically inapplicable on solutions of nonlinear systems with singular Jacobians. By a simple modification, a version of Newton's iteration regains its local quadratic convergence to nonisolated zeros of smooth mappings assuming the solutions are semiregular as properly defined regardless of whether the system is square, underdetermined or overdetermined .
Edit intent: meaning-changed
Original:  With a simple modification, a version of Newton's iteration regains its local quadratic convergence to nonisolated zeros of smooth mappings assuming the solutions are semiregular as properly defined regardless of whether the system is square, underdetermined or overdetermined  .
Revised:  With a simple modification, a novel extension of Newton's iteration regains its local quadratic convergence to nonisolated zeros of smooth mappings assuming the solutions are semiregular as properly defined regardless of whether the system is square, underdetermined or overdetermined .
Edit intent: clarity
Original:  With a simple modification, a version of Newton's iteration regains its local quadratic convergence to nonisolated zeros of smooth mappings assuming the solutions are semiregular as properly defined regardless of whether the system is square, underdetermined or overdetermined  .
Revised:  With a simple modification, a version of Newton's iteration regains its local quadratic convergence toward nonisolated solutions that are semiregular as properly defined regardless of whether the system is square, underdetermined or overdetermined .
Edit intent: clarity
Original:  With a simple modification, a version of Newton's iteration regains its local quadratic convergence to nonisolated zeros of smooth mappings assuming the solutions are semiregular as properly defined regardless of whether the system is square, underdetermined or overdetermined  .
Revised:  With a simple modification, a version of Newton's iteration regains its local quadratic convergence to nonisolated zeros of smooth mappings assuming the solutions are semiregular as properly defined regardless of whether the system is square, underdetermined or overdetermined while Jacobians can be rank-deficient .
Edit intent: meaning-changed
Original:  Even if the given system is perturbed so that the nonisolated solution disappears, the iteration still locally converges to a stationary point that approximates a  solution of the underlying system with an error bound in the same order of the data accuracy.
Revised:  When a system is perturbed so that the nonisolated solution disappears, the iteration still locally converges to a stationary point that approximates a solution of the underlying system with an error bound in the same order of the data accuracy.
Edit intent: clarity
Original:  Even if the given system is perturbed so that the nonisolated solution disappears, the iteration still locally converges to a stationary point that approximates a  solution of the underlying system with an error bound in the same order of the data accuracy.
Revised:  Even if the given system is perturbed , its nonisolated solutions can be altered substantially or even disappear. The iteration still locally converges to a stationary point that approximates a solution of the underlying system with an error bound in the same order of the data accuracy.
Edit intent: clarity
Original:  Even if the given system is perturbed so that the nonisolated solution disappears, the iteration still locally converges to a stationary point that approximates a  solution of the underlying system with an error bound in the same order of the data accuracy.
Revised:  Even if the given system is perturbed so that the nonisolated solution disappears, the iteration still locally converges to a stationary point that approximates a singular solution of the underlying system with an error bound in the same order of the data accuracy.
Edit intent: meaning-changed
Original: We extend the Hierarchical Factor Segmentation(HFS) algorithm for discovering multiple volatility states process hidden within each individual S P500 stock's return time series. Then we develop an associative measure to link stocks into directed networks of various scales of associations. Such networks shed lights on which stocks would likely stimulate or even promote, if not cause, volatility on other linked stocks. Our computing endeavors starting from encoding events of large return on the original time axis to transform the original return time series into a recurrence-time process on discrete-time-axis.
Revised: We extend the Hierarchical Factor Segmentation(HFS) algorithm for discovering multiple volatility states process hidden within each individual S P500 stock's dynamics. Such risk has been received huge amounts of attention from diverse financial researchers. By following the concept of regime-switching model, we proposed a non-parametric approach, named encoding-and-decoding, to discover multiple volatility states embedded within a discrete time series of stock returns. The encoding is performed across the entire span of temporal time points for relatively extreme events with respect to a chosen quantile-based threshold. As such the return time series into a recurrence-time process on discrete-time-axis.
Edit intent: meaning-changed
Original:  Our computing endeavors starting from encoding events of large return on the original time axis to transform the original return time series into a recurrence-time process on discrete-time-axis. By adopting BIC and clustering analysis, we identify potential multiple volatility states, and then apply the extended HFS algorithm on the recurrence time series to discover its underlying volatility state process. Our decoding approach is found favorably compared with Viterbi's in experiments involving both light and heavy tail distributions.
Revised:  Our computing endeavors starting from encoding events of large return on the original time axis to transform the original return time series is transformed into Bernoulli-variable processes. In the decoding phase, we computationally seek for locations of change points via estimations based on a new searching algorithm conjunction to the Bayesian information criterion applied on the observed collection of recurrence times upon the binary process. Besides the independence required for building the Geometric distributional likelihood function, the proposed approach can functionally partition the entire return time series into a collection of homogeneous segments without any assumptions of dynamic structure and underlying distributions. In the numerical experiments, our approach is found favorably compared with Viterbi's in experiments involving both light and heavy tail distributions.
Edit intent: meaning-changed
Original:  Our decoding approach is found favorably compared with Viterbi's in experiments involving both light and heavy tail distributions. After recovering the volatility state process back to the original time-axis, we decode and represent stock dynamics of each stock . Our measurement of association is measured through overlapping  concurrent volatility states upon a chosen window.
Revised:  Our decoding approach is found favorably compared with Viterbi's under Hidden Markov Model (HMM) settings. In the real data applications, volatility dynamics of every single stock of S concurrent volatility states upon a chosen window.
Edit intent: meaning-changed
Original:  Our measurement of association is measured through overlapping  concurrent volatility states upon a chosen window. Consequently, we establish data-driven associative networks for S &P500 stocks to discover their global dependency relational groupings with respect to various strengths of links .
Revised:  Our measurement of association is measured through overlapping concurrent volatility states . Finally, various networks dealing with distinct financial implications are consequently established to represent different aspects of global connectivity among all stocks in S &P500 stocks to discover their global dependency relational groupings with respect to various strengths of links .
Edit intent: meaning-changed
Original: To reduce Operation and Maintenance (O&M) costs on offshore wind farms, wherein 80\% of the O&M cost relates to deploying personnel, the offshore wind sector looks to robotics and Artificial Intelligence ( AI ) for solutions.
Revised: To reduce Operation and Maintenance (O&M) costs on offshore wind farms, wherein 80\% of the O&M cost relates to deploying personnel, the offshore wind sector looks to Robotics and Artificial Intelligence ( AI ) for solutions.
Edit intent: fluency
Original: To reduce Operation and Maintenance (O&M) costs on offshore wind farms, wherein 80\% of the O&M cost relates to deploying personnel, the offshore wind sector looks to robotics and Artificial Intelligence ( AI ) for solutions.
Revised: To reduce Operation and Maintenance (O&M) costs on offshore wind farms, wherein 80\% of the O&M cost relates to deploying personnel, the offshore wind sector looks to robotics and Artificial Intelligence ( RAI ) for solutions.
Edit intent: meaning-changed
Original:  We synchronize digital models of the robot, environment and infrastructure and integrate front-end analytics and bidirectional communication for autonomous adaptive mission planning and situation reporting to a remote operator.
Revised:  To achieve this, a Symbiotic Digital Architecture (SDA) was developed to synchronize digital models of the robot, environment and infrastructure and integrate front-end analytics and bidirectional communication for autonomous adaptive mission planning and situation reporting to a remote operator.
Edit intent: meaning-changed
Original:  We  analyze the mission status and diagnostics of critical sub-systems within the robot to provide automatic updates to our  run-time reliability ontology , enabling faults to be translated into failure modes for decision making during the mission.
Revised:  We demonstrate an asset inspection mission within a confined space through collaborative governance (internal and external symbiosis) via decision-making processes and the associated structures. We create a hyper enabled human interaction capability to analyze the mission status and diagnostics of critical sub-systems within the robot to provide automatic updates to our run-time reliability ontology , enabling faults to be translated into failure modes for decision making during the mission.
Edit intent: meaning-changed
Original:  We  analyze the mission status and diagnostics of critical sub-systems within the robot to provide automatic updates to our  run-time reliability ontology , enabling faults to be translated into failure modes for decision making during the mission.
Revised:  We analyze the mission status , diagnostics of critical sub-systems within the robot to provide automatic updates to our run-time reliability ontology , enabling faults to be translated into failure modes for decision making during the mission.
Edit intent: coherence