wanyu/IteraTeR_full_sent huggingface dataset:
Original: }}  that Floor-ReLU networks with width \max\{d,\, 5N+13\} and depth 64dL+3 can pointwise approximate a Lipschitz continuous } function f on [0,1]^d with an exponential approximation rate 3 \mu\sqrt{d\,N}  ^{-  \sqrt{L}}, where \mu is the Lipschitz constantof f. {  More generally for an arbitrary continuous function f on [0,1]^d with a modulus of continuity \omega_f(\cdot), the constructive approximation rate is \omega_f(\sqrt{d}\,N^{-\sqrt{L}})+2\omega_f(\sqrt{d}){N^{-\sqrt{L}}}.
Revised: }} that Floor-ReLU networks with width \max\{d,\, 5N+13\} and depth 64dL+3 can pointwise approximate a Lipschitz continuous } function f on [0,1]^d with an exponential approximation rate 3 \mu\sqrt{d\,N} ^{- \sqrt{L}}, where \mu is the Lipschitz constantof f. {\"o More generally for an arbitrary continuous function f on [0,1]^d with a modulus of continuity \omega_f(\cdot), the constructive approximation rate is \omega_f(\sqrt{d}\,N^{-\sqrt{L}})+2\omega_f(\sqrt{d}){N^{-\sqrt{L}}}.
Edit intent: clarity
Original: }}  that Floor-ReLU networks with width \max\{d,\, 5N+13\} and depth 64dL+3 can pointwise approximate a Lipschitz continuous } function f on [0,1]^d with an exponential approximation rate 3 \mu\sqrt{d\,N}  ^{-  \sqrt{L}}, where \mu is the Lipschitz constantof f. {  More generally for an arbitrary continuous function f on [0,1]^d with a modulus of continuity \omega_f(\cdot), the constructive approximation rate is \omega_f(\sqrt{d}\,N^{-\sqrt{L}})+2\omega_f(\sqrt{d}){N^{-\sqrt{L}}}.
Revised: }} that Floor-ReLU networks with width \max\{d,\, 5N+13\} and depth 64dL+3 can pointwise approximate a Lipschitz continuous } function f on [0,1]^d with an exponential approximation rate 3 \mu\sqrt{d\,N} ^{- \sqrt{L}}, where \mu is the Lipschitz constantof f. { lder order and constant, respectively. More generally for an arbitrary continuous function f on [0,1]^d with a modulus of continuity \omega_f(\cdot), the constructive approximation rate is \omega_f(\sqrt{d}\,N^{-\sqrt{L}})+2\omega_f(\sqrt{d}){N^{-\sqrt{L}}}.
Edit intent: meaning-changed
Original:  As a consequence, this new network overcomes  the curse of dimensionality in approximation power since this approximation order is\le  } essentially \sqrt{d} times a function of N and L independent of d .
Revised:  As a consequence, this new class of networks the curse of dimensionality in approximation power since this approximation order is\le } essentially \sqrt{d} times a function of N and L independent of d .
Edit intent: clarity
Original:  As a consequence, this new network overcomes  the curse of dimensionality in approximation power since this approximation order is\le  } essentially \sqrt{d} times a function of N and L independent of d .
Revised:  As a consequence, this new network overcomes overcome the curse of dimensionality in approximation power since this approximation order is\le } essentially \sqrt{d} times a function of N and L independent of d .
Edit intent: fluency
Original:  As a consequence, this new network overcomes  the curse of dimensionality in approximation power since this approximation order is\le  } essentially \sqrt{d} times a function of N and L independent of d .
Revised:  As a consequence, this new network overcomes the curse of dimensionality in approximation power when the variation of \omega_f(r) as r\rightarrow 0 is moderate (e.g., \omega_f(r)\le } essentially \sqrt{d} times a function of N and L independent of d .
Edit intent: meaning-changed
Original:  As a consequence, this new network overcomes  the curse of dimensionality in approximation power since this approximation order is\le  } essentially \sqrt{d} times a function of N and L independent of d .
Revised:  As a consequence, this new network overcomes the curse of dimensionality in approximation power since this approximation order is\le r^\alpha for H } essentially \sqrt{d} times a function of N and L independent of d .
Edit intent: meaning-changed
Original:  As a consequence, this new network overcomes  the curse of dimensionality in approximation power since this approximation order is\le  } essentially \sqrt{d} times a function of N and L independent of d .
Revised:  As a consequence, this new network overcomes the curse of dimensionality in approximation power since this approximation order is\le \"o} essentially \sqrt{d} times a function of N and L independent of d .
Edit intent: meaning-changed
Original:  As a consequence, this new network overcomes  the curse of dimensionality in approximation power since this approximation order is\le  } essentially \sqrt{d} times a function of N and L independent of d .
Revised:  As a consequence, this new network overcomes the curse of dimensionality in approximation power since this approximation order is\le }lder continuous functions), since the major term to be concerned in our approximation rate is essentially \sqrt{d} times a function of N and L independent of d .
Edit intent: meaning-changed
Original:  As a consequence, this new network overcomes  the curse of dimensionality in approximation power since this approximation order is\le  } essentially \sqrt{d} times a function of N and L independent of d .
Revised:  As a consequence, this new network overcomes the curse of dimensionality in approximation power since this approximation order is\le } essentially \sqrt{d} times a function of N and L independent of d within the modulus of continuity.
Edit intent: meaning-changed
Original: In this paper, we focus on structure-preserving model order reduction (SPMOR) of the second-order system using the Iterative Rational Krylov Algorithm (IRKA).
Revised: In this paper, we focus on the efficient techniques to estimate the \mathcal{H (SPMOR) of the second-order system using the Iterative Rational Krylov Algorithm (IRKA).
Edit intent: meaning-changed
Original: In this paper , we focus on the efficient techniques to estimate the H_2 optimal Structure-Preserving Model Order Reduction (SPMOR) of the second-order systems using the Iterative Rational Krylov Algorithm (IRKA).
Revised: This paper focuses on exploring efficient ways to find H_2 optimal Structure-Preserving Model Order Reduction (SPMOR) of the second-order systems using the Iterative Rational Krylov Algorithm (IRKA).
Edit intent: clarity
Original: In this paper , we focus on the efficient techniques to estimate the H_2 optimal Structure-Preserving Model Order Reduction (SPMOR) of the second-order systems using the Iterative Rational Krylov Algorithm (IRKA).
Revised: In this paper , we focus on the efficient techniques to estimate the H_2 optimal Structure-Preserving Model Order Reduction (SPMOR) of the second-order systems via interpolatory projection-based method Iterative Rational Krylov Algorithm (IRKA).
Edit intent: meaning-changed
Original:  In general , the classical IRKA can be applied to the second-order system by converting it into an equivalent first-order form and get the reduced model in a first-order form. In this case, the reduced model can not preserve the structure of the second-order system which is however necessary for further manipulation. Here we develop IRKA based algorithms that enable us to generate approximate reduced second-order systems without explicitly converting the systems into a first-order form .
Revised:  In general , the classical IRKA can be applied to the second-order system by converting it into an equivalent first-order form and get the reduced model in a first-order reduced models. The drawbacks of that of the technique are failure of structure preservation and abolishing the properties of the original models, which are the key factors for some of the physical applications. To surpass those issues, we introduce IRKA based techniques that enable us to generate approximate reduced second-order systems without explicitly converting the systems into a first-order form .
Edit intent: coherence
Original:  On the other hand, there are very challenging tasks to find reduced-order form of a large-scale system with a minimized \mathcal{H}_2 error norm and attain the rapid rate of convergence.
Revised:  On the other hand, there are very challenging tasks to the Model Order Reduction (MOR) of the large-scale system with a minimized \mathcal{H}_2 error norm and attain the rapid rate of convergence.
Edit intent: clarity
Original:  On the other hand, there are very challenging tasks to find reduced-order form of a large-scale system with a minimized \mathcal{H}_2 error norm and attain the rapid rate of convergence.
Revised:  On the other hand, there are very challenging tasks to find reduced-order form of a large-scale second-order systems with the optimal \mathcal{H}_2 error norm and attain the rapid rate of convergence.
Edit intent: clarity
Original:  To overcome these problems, this paper discusses competent techniques to determine the optimal \mathcal{H}_2 error norm efficiently for the second-order system. The efficiency and applicability of the proposed techniques are validated by applying them to several large-scale dynamical systems .
Revised:  To overcome these problems, this paper discusses competent techniques to determine the optimal \mathcal{H}_2 error norm efficiently for the second-order systems. The applicability and efficiency of the proposed techniques are validated by applying them to several large-scale dynamical systems .
Edit intent: fluency
Original:  The efficiency and applicability of the proposed techniques are validated by applying them to several large-scale dynamical systems . The computation is done numerically and the achieved results are discussed in both tabular and graphical approaches.
Revised:  The efficiency and applicability of the proposed techniques are validated by applying them to several large-scale systems extracted form engineering applications. The computations are done numerically using MATLAB simulation and the achieved results are discussed in both tabular and graphical approaches.
Edit intent: meaning-changed
Original:  The study explores whether the causal relationships  among the growth rate of confirmed cases ( GrowthC ), exchange rate (GEX) and SENSEX value (GSENSEX) are remaining the same across different pre and post-lockdown phases, attempting to capture any potential changes over time via the Vector Auto Regressive (VAR) models.
Revised:  The study explores whether the causal relationships and directions among the growth rate of confirmed cases ( GrowthC ), exchange rate (GEX) and SENSEX value (GSENSEX) are remaining the same across different pre and post-lockdown phases, attempting to capture any potential changes over time via the Vector Auto Regressive (VAR) models.
Edit intent: meaning-changed
Original:  The study explores whether the causal relationships  among the growth rate of confirmed cases ( GrowthC ), exchange rate (GEX) and SENSEX value (GSENSEX) are remaining the same across different pre and post-lockdown phases, attempting to capture any potential changes over time via the Vector Auto Regressive (VAR) models.
Revised:  The study explores whether the causal relationships among the growth rate of confirmed cases ( GROWTHC ), exchange rate (GEX) and SENSEX value (GSENSEX) are remaining the same across different pre and post-lockdown phases, attempting to capture any potential changes over time via the Vector Auto Regressive (VAR) models.
Edit intent: meaning-changed
Original:  The study explores whether the causal relationships  among the growth rate of confirmed cases ( GrowthC ), exchange rate (GEX) and SENSEX value (GSENSEX) are remaining the same across different pre and post-lockdown phases, attempting to capture any potential changes over time via the Vector Auto Regressive (VAR) models.
Revised:  The study explores whether the causal relationships among the growth rate of confirmed cases ( GrowthC ), exchange rate (GEX) and SENSEX value (GSENSEX) are remaining the same across different pre and post-lockdown phases, attempting to capture any potential changes over time via the vector autoregressive (VAR) models.
Edit intent: clarity
Original:  However, on applying a VAR model, it is observed that an increase in the confirmed COVID-19 cases causes no significant change in the values of the exchange rate and SENSEX index.
Revised:  However, on applying a vector autoregressive (VAR) model, it is observed that an increase in the confirmed COVID-19 cases causes no significant change in the values of the exchange rate and SENSEX index.
Edit intent: meaning-changed
Original:  The result varies if the analysis is split across different time periods - before lockdown, first phase of lockdownand extension of lockdown. To compare the three periods, we had undertaken five rounds of analyses . Nuanced and sensible interpretations of the numeric results indicate significant variability across time in terms of the relation between the variables of interest.
Revised:  The result varies if the analysis is split across different time periods - before lockdown, the four phases of lockdown, and the first phase of unlock . Nuanced and sensible interpretations of the numeric results indicate significant variability across time in terms of the relation between the variables of interest.
Edit intent: meaning-changed
Original:  However, a careful analysis of existing literature reveals that prior studies observed improvements due to explanations only when the AI, alone, outperformed both the human and the best human-AI team. This raises an important question: can explanations lead to complementary performance, i.e., with accuracy higher than both the human and the AI working alone?
Revised:  However, a careful analysis of existing literature reveals that prior studies observed improvements due to explanations only when the AI, alone, outperformed both the human and the best team. Can explanations help lead to complementary performance, i.e., with accuracy higher than both the human and the AI working alone?
Edit intent: clarity
Original:  This raises an important question: can explanations lead to complementary performance, i.e., with accuracy higher than both the human and the AI working alone? We address this question by devising comprehensive studies on human-AI teaming, where participants solve a task with help from an AI system without explanations and from one with varying types of AI explanation support. We carefully controlled to ensure comparable human and AI accuracy across experiments on three NLP datasets (two for sentiment analysis and one for question answering ).
Revised:  This raises an important question: can explanations lead to complementary performance, i.e., with accuracy higher than both the human and the AI working solo? We conduct mixed-method user studies on three datasets, where an AI with accuracy comparable to humans helps participants solve a task (explaining itself in some conditions ).
Edit intent: clarity
Original:  While we found complementary improvements from AI augmentation, they were not increased by state-of-the-art explanationscompared to simpler strategies, such as displaying the AI's confidence. We show that explanations increase the chance that humans will accept the AI's recommendation regardless of whether the AI is correct.
Revised:  While we found complementary improvements from AI augmentation, they were not increased by explanations. Rather, explanations increased the chance that humans will accept the AI's recommendation regardless of whether the AI is correct.
Edit intent: clarity
Original:  We show that explanations increase the chance that humans will accept the AI's recommendation regardless of whether the AI is correct. While this clarifies the gains in team performance from explanations in prior work, it poses new challenges for human-centered AI: how can we best design systems to produce complementary performance?
Revised:  We show that explanations increase the chance that humans will accept the AI's recommendation , regardless of its correctness. Our result poses new challenges for human-centered AI: how can we best design systems to produce complementary performance?
Edit intent: coherence
Original: We discuss a stochastic model to assess cumulative excess deaths during Covid-19-like epidemics for various non-pharmaceutic interventions. The model simulates three interrelated stochastic processes: epidemic spreading, availability of respiratory ventilators and changes in death statistics. Epidemic may spread either locally or globally. The local mode simulates virus transmission through contacts in the vicinity of the place of residence while the global mode simulates virus transmission through social mixing in public places  , sport arenas, airports, etc  , where many people meet, who live in remote geographic locations.
Revised: We discuss a stochastic model to assess cumulative excess deaths during Covid-19-like epidemics for various non-pharmaceutical intervention strategies. We consider local and non-local modes of disease transmission. The first simulates transmission through social contacts in the vicinity of the place of residence while the global mode simulates virus transmission through social mixing in public places , sport arenas, airports, etc , where many people meet, who live in remote geographic locations.
Edit intent: clarity
Original:  The local mode simulates virus transmission through contacts in the vicinity of the place of residence while the global mode simulates virus transmission through social mixing in public places  , sport arenas, airports, etc  , where many people meet, who live in remote geographic locations.
Revised:  The local mode simulates virus transmission through contacts in the vicinity of the place of residence while the second through social contacts in public places , sport arenas, airports, etc , where many people meet, who live in remote geographic locations.
Edit intent: clarity
Original:  The local mode simulates virus transmission through contacts in the vicinity of the place of residence while the global mode simulates virus transmission through social mixing in public places  , sport arenas, airports, etc  , where many people meet, who live in remote geographic locations.
Revised:  The local mode simulates virus transmission through contacts in the vicinity of the place of residence while the global mode simulates virus transmission through social mixing in public places : schools, hospitals , sport arenas, airports, etc , where many people meet, who live in remote geographic locations.
Edit intent: meaning-changed
Original:  The local mode simulates virus transmission through contacts in the vicinity of the place of residence while the global mode simulates virus transmission through social mixing in public places  , sport arenas, airports, etc  , where many people meet, who live in remote geographic locations.
Revised:  The local mode simulates virus transmission through contacts in the vicinity of the place of residence while the global mode simulates virus transmission through social mixing in public places , airports, etc , where many people meet, who live in remote geographic locations.
Edit intent: clarity
Original:  The local mode simulates virus transmission through contacts in the vicinity of the place of residence while the global mode simulates virus transmission through social mixing in public places  , sport arenas, airports, etc  , where many people meet, who live in remote geographic locations.
Revised:  The local mode simulates virus transmission through contacts in the vicinity of the place of residence while the global mode simulates virus transmission through social mixing in public places , sport arenas, airports, etc . , where many people meet, who live in remote geographic locations.
Edit intent: fluency
Original:  We also assume that the virus leads to severe acute respiratory syndrome in about one percent of cases, which in turn almost surely lead to respiratory default and death, unless the patient receives an appropriate medical treatment supported by respiratory ventilation.
Revised:  We also assume that the virus leads to severe acute respiratory syndrome in about one percent of cases, which are likely to lead to respiratory default and death, unless the patient receives an appropriate medical treatment supported by respiratory ventilation.
Edit intent: clarity
Original:  We also assume that the virus leads to severe acute respiratory syndrome in about one percent of cases, which in turn almost surely lead to respiratory default and death, unless the patient receives an appropriate medical treatment supported by respiratory ventilation. For other parameters , like mortality rate or the number of respiratory ventilators per million of inhabitants, we take values typical for developed countries.
Revised:  We also assume that the virus leads to severe acute respiratory syndrome in about one percent of cases, which in turn almost surely lead to respiratory default and death, unless the patient receives an appropriate medical treatment . The~healthcare system capacity is simulated by the availability of respiratory ventilators or intensive care beds. Some parameters of the model , like mortality rate or the number of respiratory ventilators per million of inhabitants, we take values typical for developed countries.
Edit intent: meaning-changed
Original:  For other parameters , like mortality rate or the number of respiratory ventilators per million of inhabitants, we take values typical for developed countries. We simulate populations of 10^5-10^6 people. We compare different strategies: do-nothing , social distancing , reduction of social mixingand lockdown, assuming that there is no vaccine and no efficient medicine .
Revised:  For other parameters , like mortality rate or the number of respiratory ventilators per 100000 inhabitants, are chosen to simulate the real values for the USA and Poland. In the simulations we compare ` do-nothing , social distancing , reduction of social mixingand lockdown, assuming that there is no vaccine and no efficient medicine .
Edit intent: meaning-changed
Original:  We compare different strategies: do-nothing , social distancing , reduction of social mixingand lockdown, assuming that there is no vaccine and no efficient medicine .
Revised:  We compare different strategies: do-nothing ' strategy with mitigation strategies based on social distancing and reducing social mixing. We study epidemics in the pre-vaccine era, where immunity is obtained only by infection. The model applies only to epidemics for which reinfections are rare and can be neglected .
Edit intent: meaning-changed
Original:  The results of the simulations show that strategies that slow down the spread of epidemic too much are inefficient in reducing the cumulative excess of deaths . A hybrid strategy in which lockdown is in place for some time and is then completely released is inefficient as well .
Revised:  The results of the simulations show that strategies that slow down the spread of epidemic too much in the early stages do not significantly reduce the overall number of deaths in the long term, but increase the duration of the epidemic. In particular, a~hybrid strategy where lockdown is held for some time and is then completely released is inefficient as well .
Edit intent: meaning-changed