wanyu/IteraTeR_full_sent huggingface dataset:
Original: We derive the variational formulation of an anisotropic gradient damage model with different behaviour at traction and compression and a state dependent dissipation potential by applying the energetic formulation of rate-independent processes .
Revised: We derive the variational formulation of an anisotropic gradient damage model by applying the energetic formulation of rate-independent processes and obtain a regularized formulation of fracture. The model exhibits different behavior at traction and compression and a state dependent dissipation potential by applying the energetic formulation of rate-independent processes .
Edit intent: meaning-changed
Original:  We will also show how such formulation provides the natural framework for setting up a consistent numerical scheme with the underlying variational structure and for the derivation of additional necessary conditions of global optimality in the form of a two-sided energetic inequality.
Revised:  We will show how such formulation provides the natural framework for setting up a consistent numerical scheme with the underlying variational structure and for the derivation of additional necessary conditions of global optimality in the form of a two-sided energetic inequality.
Edit intent: coherence
Original:  We will observe that by including the two-sided energetic inequality in our solution method, we describe, for some of the benchmark problems, an equilibrium path when  damage starts to manifest, which is different from the one obtained by solving simply the stationariety conditions of the underlying functional.
Revised:  We will observe that by including the two-sided energetic inequality in our solution method, we describe, for some of the benchmark problems, an equilibrium path when the damage starts to manifest, which is different from the one obtained by solving simply the stationariety conditions of the underlying functional.
Edit intent: fluency
Original:  We will observe that by including the two-sided energetic inequality in our solution method, we describe, for some of the benchmark problems, an equilibrium path when  damage starts to manifest, which is different from the one obtained by solving simply the stationariety conditions of the underlying functional.
Revised:  We will observe that by including the two-sided energetic inequality in our solution method, we describe, for some of the benchmark problems, an equilibrium path when damage starts to manifest, which is different from the one obtained by solving simply the stationarity conditions of the underlying functional.
Edit intent: fluency
Original:  Our proposed method allows information integration beyond local windows, which is especially beneficial for question answering (QA) and language modeling tasks that rely on long-range dependencies.
Revised:  The proposed framework is pivoted on two unique types of Transformer layer: Sliding-Window Layer and Cluster-Former Layer, which encode local sequence information and global context jointly and iteratively. This new design allows information integration beyond local windows, which is especially beneficial for question answering (QA) and language modeling tasks that rely on long-range dependencies.
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Original:  To achieve this pass bound, our algorithm combines a number of techniques  from different fields such as the interior point method (IPM), symmetric diagonally dominant (SDD ) system solving , the isolation lemma, and LP duality.
Revised:  Our streaming algorithm constructs a subgraph with n edges of the input graph in from different fields such as the interior point method (IPM), symmetric diagonally dominant (SDD ) system solving , the isolation lemma, and LP duality.
Edit intent: meaning-changed
Original:  To achieve this pass bound, our algorithm combines a number of techniques  from different fields such as the interior point method (IPM), symmetric diagonally dominant (SDD ) system solving , the isolation lemma, and LP duality.
Revised:  To achieve this pass bound, our algorithm combines a number of techniques (\sqrt{m from different fields such as the interior point method (IPM), symmetric diagonally dominant (SDD ) system solving , the isolation lemma, and LP duality.
Edit intent: meaning-changed
Original:  To achieve this pass bound, our algorithm combines a number of techniques  from different fields such as the interior point method (IPM), symmetric diagonally dominant (SDD ) system solving , the isolation lemma, and LP duality.
Revised:  To achieve this pass bound, our algorithm combines a number of techniques from different fields , most notably the construction of interior point method (IPM), symmetric diagonally dominant (SDD ) system solving , the isolation lemma, and LP duality.
Edit intent: meaning-changed
Original:  To achieve this pass bound, our algorithm combines a number of techniques  from different fields such as the interior point method (IPM), symmetric diagonally dominant (SDD ) system solving , the isolation lemma, and LP duality.
Revised:  To achieve this pass bound, our algorithm combines a number of techniques from different fields such as thespace-efficient interior point method (IPM), symmetric diagonally dominant (SDD ) system solving , the isolation lemma, and LP duality.
Edit intent: meaning-changed
Original:  To achieve this pass bound, our algorithm combines a number of techniques  from different fields such as the interior point method (IPM), symmetric diagonally dominant (SDD ) system solving , the isolation lemma, and LP duality.
Revised:  To achieve this pass bound, our algorithm combines a number of techniques from different fields such as the interior point method (IPM), SDD system solvers , the isolation lemma, and LP duality.
Edit intent: coherence
Original:  To the best of our knowledge, this is the first work that implements the SDD solver and IPM in the streaming model in \widetilde{O}(n) spaces for graph matrix. All the previous IPMs only focus on optimizing the running time, regardless of the space usage .
Revised:  To the best of our knowledge, this is the first work that implements the SDD solver and IPM in the streaming model in \widetilde{O}(n) spaces for graph matrices; previous IPM algorithms only focus on optimizing the running time, regardless of the space usage .
Edit intent: clarity
Original:  All the previous IPMs only focus on optimizing the running time, regardless of the space usage . The LP solver for general matrix is impossible to be implemented in%DIFDELCMD < \widetilde{O}%%% (n) spaces .
Revised:  All the previous IPMs only focus on optimizing the running time, regardless of the space usage %DIFDELCMD < \widetilde{O}%%% (n) spaces .
Edit intent: coherence
Original:  The Designer's optimization problem (designing a custom suite for the Agent so as to optimize, through the Agent's optimum reaction, the Designer's revenue), while NP-hard  , has an FPTAS.
Revised:  The Designer's optimization problem (designing a custom suite for the Agent so as to optimize, through the Agent's optimum reaction, the Designer's revenue), is NP-hard , has an FPTAS.
Edit intent: coherence
Original:  The Designer's optimization problem (designing a custom suite for the Agent so as to optimize, through the Agent's optimum reaction, the Designer's revenue), while NP-hard  , has an FPTAS.
Revised:  The Designer's optimization problem (designing a custom suite for the Agent so as to optimize, through the Agent's optimum reaction, the Designer's revenue), while NP-hard to approximate within any finite ratio; however, the special case, while still NP-hard , has an FPTAS.
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Original:  These results generalize , under mild additional assumptions, from a single Agent to a distribution of Agents with finite support . The Designer's optimization problem has abysmal "price of robustness", suggesting that learning the parameters of the problem is crucial for the Designer .
Revised:  These results generalize , under mild additional assumptions, from a single Agent to a distribution of Agents with finite support , as well as to the setting where the Designer must find the best response to the existing strategies of other Designers. We discuss other implications of our results and directions of future research .
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Original:  These surrogates have the salient feature of being essentially indistinguishable from or very close to supercomputer simulations of the Einstein equations  but can be evaluated in less than a second on a laptop.
Revised:  These surrogates have the salient feature of being essentially indistinguishable from or very close to supercomputer simulations of the Einstein equations , but can be evaluated in less than a second on a laptop.
Edit intent: fluency
Original:  These surrogates have the salient feature of being essentially indistinguishable from or very close to supercomputer simulations of the Einstein equations  but can be evaluated in less than a second on a laptop.
Revised:  These surrogates have the salient feature of being essentially indistinguishable from or very close to supercomputer simulations of the Einstein equations but can be evaluated in the order of a milisecond per multipole mode on a standard laptop.
Edit intent: meaning-changed
Original:  In this note we analyze in detail how the EIM at each iteration attempts to choose the interpolation nodes so as to make the related Vandermonde-type matrix " as invertible as possible " as well as attempting to optimize the conditioning of its inversion and minimizing a Lebesgue-type constantfor accuracy.
Revised:  In this article we clarify a common misperception of the EIM as originally introduced and used in practice in GW science. Namely, we prove that the EIM at each iteration attempts to choose the interpolation nodes so as to make the related Vandermonde-type matrix " as invertible as possible " as well as attempting to optimize the conditioning of its inversion and minimizing a Lebesgue-type constantfor accuracy.
Edit intent: meaning-changed
Original:  In this note we analyze in detail how the EIM at each iteration attempts to choose the interpolation nodes so as to make the related Vandermonde-type matrix " as invertible as possible " as well as attempting to optimize the conditioning of its inversion and minimizing a Lebesgue-type constantfor accuracy.
Revised:  In this note we analyze in detail how the EIM at each iteration chooses the interpolation nodes so as to make the related Vandermonde-type matrix " as invertible as possible " as well as attempting to optimize the conditioning of its inversion and minimizing a Lebesgue-type constantfor accuracy.
Edit intent: fluency
Original:  In this note we analyze in detail how the EIM at each iteration attempts to choose the interpolation nodes so as to make the related Vandermonde-type matrix " as invertible as possible " as well as attempting to optimize the conditioning of its inversion and minimizing a Lebesgue-type constantfor accuracy.
Revised:  In this note we analyze in detail how the EIM at each iteration attempts to choose the interpolation nodes so as to make the related Vandermonde-type matrix as invertible as possible " as well as attempting to optimize the conditioning of its inversion and minimizing a Lebesgue-type constantfor accuracy.
Edit intent: fluency
Original:  In this note we analyze in detail how the EIM at each iteration attempts to choose the interpolation nodes so as to make the related Vandermonde-type matrix " as invertible as possible " as well as attempting to optimize the conditioning of its inversion and minimizing a Lebesgue-type constantfor accuracy. We then compare through numerical experiments the EIM performance with fully optimized nested variations.
Revised:  In this note we analyze in detail how the EIM at each iteration attempts to choose the interpolation nodes so as to make the related Vandermonde-type matrix " as invertible as possible ; not necessarily optimizing its conditioning or accuracy of the interpolant as is sometimes thought. In fact, we introduce two new variations of the EIM, nested as well, which do optimize with respect to conditioning and the Lebesgue constant, respectively, and compare them through numerical experiments the EIM performance with fully optimized nested variations.
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Original:  We then compare through numerical experiments the EIM performance with fully optimized nested variations. We also discuss global optimal solutions through Fekete nodes. We find that in these experiments the EIM is actually close to optimal solutions but can be improved with small variations and relative low computational cost .
Revised:  We then compare through numerical experiments with the original EIM using GWs. Our analyses and numerical results suggest a subtle relationship between solving for the original EIM, conditioning, and the Lebesgue constant, in consonance with active research in rigorous approximation theory and related fields .
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Original: The energy dissipation is an important and essential property of classical phase-field equations . However, it is still unknown if the phase-field models with Caputo time-fractional derivative preserve this property, which is challenging due to the existence of both nonlocality and nonlinearity.
Revised: The energy dissipation is an important and essential property of classical phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the existence of both nonlocality and nonlinearity.
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Original:  However, it is still unknown if the phase-field models with Caputo time-fractional derivative preserve this property, which is challenging due to the existence of both nonlocality and nonlinearity. Our recent work shows that on the continuous level, the time-fractional energy dissipation law and the weighted energy dissipation law can be achieved.
Revised:  However, it is still unknown if the phase-field models with Caputo time-fractional derivative preserve this property, which is challenging due to the solution such as energy dissipation and maximum principle. Although the theory of energy dissipation for classical phase field models is well established, the weighted energy dissipation law can be achieved.
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Original:  Our recent work shows that on the continuous level, the time-fractional energy dissipation law and the weighted energy dissipation law can be achieved. Inspired by them, we study in this article the energy dissipation of some numerical schemes for time-fractional phase-field models , including the convex-splitting scheme, the stabilization scheme, and the scalar auxiliary variable scheme.
Revised:  Our recent work shows that on the continuous level, the time-fractional energy dissipation law and the corresponding theory for time-fractional phase-field models , including the convex-splitting scheme, the stabilization scheme, and the scalar auxiliary variable scheme.
Edit intent: clarity
Original:  Inspired by them, we study in this article the energy dissipation of some numerical schemes for time-fractional phase-field models , including the convex-splitting scheme, the stabilization scheme, and the scalar auxiliary variable scheme. Based on a lemma about a special Cholesky decomposition, it can be proved that the discrete fractional derivative of energy is nonpositive, i.e., the discrete time-fractional energy dissipation law , and that a discrete weighted energy can be constructed to be dissipative, i. e., the discrete weighted energy dissipation law.
Revised:  Inspired by them, we study in this article the energy dissipation of some numerical schemes for time-fractional phase-field models is still incomplete. In this article, we study certain nonlocal-in-time energies using the first-order stabilized semi-implicit L1 scheme. In particular, we will establish a discrete fractional energy law and a discrete weighted energy can be constructed to be dissipative, i. e., the discrete weighted energy dissipation law.
Edit intent: meaning-changed
Original:  Based on a lemma about a special Cholesky decomposition, it can be proved that the discrete fractional derivative of energy is nonpositive, i.e., the discrete time-fractional energy dissipation law , and that a discrete weighted energy can be constructed to be dissipative, i. e., the discrete weighted energy dissipation law. In addition, some numerical tests are provided } to verify our theoretical analysis.
Revised:  Based on a lemma about a special Cholesky decomposition, it can be proved that the discrete fractional derivative of energy is nonpositive, i.e., the discrete time-fractional energy dissipation law , and that a discrete weighted energy law. The extension for a (2- } to verify our theoretical analysis.
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Original: Copulas are becoming an essential tool in analyzing data and knowing local copula bounds with a fixed value of a given measure of association is turning into a prerequisite in the early stage of exploratory data analysis .
Revised: Copulas are becoming an essential tool in analyzing data thus encouraging interest in related questions. In the early stage of exploratory data analysis, say, it is helpful to know local copula bounds with a fixed value of a given measure of association is turning into a prerequisite in the early stage of exploratory data analysis .
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Original:  The present study demonstrates the potential of low dose BMP-2 treatment via tissue engineering approach, which amalgamates 3-D macro/microporous-nanofibrous bacterial cellulose (mNBC) scaffolds and low dose BMP-2 primed murine mesenchymal stem cells (C3H10T1/2 cells).
Revised:  The present study explores the potential of low dose BMP-2 treatment via tissue engineering approach, which amalgamates 3-D macro/microporous-nanofibrous bacterial cellulose (mNBC) scaffolds and low dose BMP-2 primed murine mesenchymal stem cells (C3H10T1/2 cells).
Edit intent: clarity
Original:  Initial studies on cell-scaffold interaction using unprimed C3H10T1/2 cells confirmed that scaffolds provided a propitious environment for cell adhesion, growth, and infiltration, owing to its ECM-mimicking nano-macro/micro architecture.
Revised:  Initial studies on cell-scaffold interaction using unprimed C3H10T1/2 cells confirmed that scaffolds provided a propitious environment for cell adhesion, growth, and infiltration, owing to its ECM-mimicking nano-micro-macro architecture.
Edit intent: clarity
Original: Class-conditional language models ( CC-LMs) can be used to generate natural language with specific attributes, such as style or sentiment, by conditioning on an attribute label, or control code. However, we find that these models struggle to control generation when applied to out-of-domain prompts or unseen control codes. To overcome these limitations, we propose generative discriminator (GeDi ) guided contrastive generation, which uses CC-LMs as generative discriminators (GeDis) to efficiently guide generation from a (potentially much larger) LM towards a desired attribute.
Revised: Class-conditional language models ( LMs) are able to imitate the distribution of natural language well enough to generate realistic text, it is difficult to control which regions of the distribution they generate. This is especially problematic because datasets used for training large LMs usually contain significant toxicity, hate, bias, and negativity. We propose GeDi as an efficient method for using smaller LMs as generative discriminators to guide generation from a (potentially much larger) LM towards a desired attribute.
Edit intent: coherence
Original:  To overcome these limitations, we propose generative discriminator (GeDi ) guided contrastive generation, which uses CC-LMs as generative discriminators (GeDis) to efficiently guide generation from a (potentially much larger) LM towards a desired attribute. In our human evaluation experiments, we show that GeDis trained for sentiment control on movie reviews are able to control the tone of book text.
Revised:  To overcome these limitations, we propose generative discriminator (GeDi ) guided contrastive generation, which uses CC-LMs as generative discriminators (GeDis) to efficiently guide generation from large LMs to make them safer and more controllable. GeDi guides generation at each step by computing classification probabilities for all possible next tokens via Bayes rule by normalizing over two class-conditional distributions; one conditioned on the desired attribute, or control code, and another conditioned on the undesired attribute, or anti control code. We find that GeDi gives stronger controllability than the state of the art method while also achieving generation speeds more than 30 times faster. Additionally, training GeDi on movie reviews are able to control the tone of book text.
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Original:  In our human evaluation experiments, we show that GeDis trained for sentiment control on movie reviews are able to control the tone of book text. We also demonstrate that GeDis are able to detoxify generation and control topic while maintaining the same level of linguistic acceptability as direct generation from GPT-2 (1.5 B parameters).
Revised:  In our human evaluation experiments, we show that GeDis trained for sentiment control on only four topics allows us to controllably generate new topics zero-shot from just a keyword, unlocking a new capability that previous controllable generation methods do not have. Lastly, we show that GeDi can make GPT-2 (1.5 B parameters).
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Original:  We also demonstrate that GeDis are able to detoxify generation and control topic while maintaining the same level of linguistic acceptability as direct generation from GPT-2 (1.5 B parameters). Lastly, we show that a GeDi trained on only 4 topics can generalize to new control codes from word embeddings, allowing it to guide generation towards wide array of topics .
Revised:  We also demonstrate that GeDis are able to detoxify generation and control topic while maintaining the same level of linguistic acceptability as direct generation from GPT-2 (1.5 B parameters) significantly less toxic without sacrificing linguistic quality, making it by far the most practical existing method for detoxifying large language models while maintaining a fast generation speed .
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Original:  The latter provides a theoretical justification for the use of vector copulas to characterize nonlinear or rank dependence between a finite number of random vectors (robust to within vector dependence), and to construct multivariate distributions with any given non-overlapping multivariate marginals.
Revised:  The latter provides a theoretical justification for the use of vector copulas to characterize nonlinear or rank dependence between a finite number of random vectors (robust to within vector dependence), and to construct multivariate distributions with any given non overlapping multivariate marginals.
Edit intent: fluency
Original:   We illustrate our approach by minimizing the total time required to eradicate COVID-19 within the Susceptible-Exposed-Infected-Recovered (SEIR) model proposed by Kissler et al. (March, 2020) .
Revised:  In contrast to past approaches for policy optimization based on control theory, our framework can deal with arbitrary uncertainties on the initial conditions and model parameters controlling the spread of the disease. In addition, our methods allow for optimization over weekly-constant policies, specified by either continuous or discrete government measures (e.g.: lockdown on/off). We illustrate our approach by minimizing the total time required to eradicate COVID-19 within the Susceptible-Exposed-Infected-Recovered (SEIR) model proposed by Kissler et al. (March, 2020) .
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