wanyu/IteraTeR_v2 huggingface dataset:
Original:  V ^{-1}u,v \in \mathcal{V} |u \vert{u} \rangle %DIFDELCMD < \langle %%% v |, with V = |\mathcal{V \langle{v}\vert . Requiring only that W have a constant lower bound on its spectral gap and upper bound \kappa on its spectral ratio, our QAO algorithm returns m using \Gamma with probability (1-\epsilon)(1-e^{-1/\epsilon}) in time \widetilde{\mathcal{O}}(\epsilon ^{-1[\sqrt{V} + (\kappa-1)^{2/3}V^{2/3}]} [\sqrt{|\mathcal{V}|} + (\kappa-1)^{2/3}|\mathcal{V}|^{2/3}]} ).
Revised:  V ^{-1}u,v \in \mathcal{V} |u \vert{u} \rangle %DIFDELCMD < \langle %%% v |, with V = |\mathcal{V \langle{v}\vert . Requiring only that W have a constant lower bound on its spectral gap and upper bound \kappa on its spectral ratio, our QAO algorithm returns m using \Gamma with probability (1-\epsilon)(1-e^{-1/\epsilon}) in time \widetilde{\mathcal{O}}(\epsilon [\sqrt{V} + (\kappa-1)^{2/3}V^{2/3}]} [\sqrt{|\mathcal{V}|} + (\kappa-1)^{2/3}|\mathcal{V}|^{2/3}]} ).
Edit intent: fluency
Original:  V ^{-1}u,v \in \mathcal{V} |u \vert{u} \rangle %DIFDELCMD < \langle %%% v |, with V = |\mathcal{V \langle{v}\vert . Requiring only that W have a constant lower bound on its spectral gap and upper bound \kappa on its spectral ratio, our QAO algorithm returns m using \Gamma with probability (1-\epsilon)(1-e^{-1/\epsilon}) in time \widetilde{\mathcal{O}}(\epsilon ^{-1[\sqrt{V} + (\kappa-1)^{2/3}V^{2/3}]} [\sqrt{|\mathcal{V}|} + (\kappa-1)^{2/3}|\mathcal{V}|^{2/3}]} ).
Revised:  V ^{-1}u,v \in \mathcal{V} |u \vert{u} \rangle %DIFDELCMD < \langle %%% v |, with V = |\mathcal{V \langle{v}\vert . Requiring only that W have a constant lower bound on its spectral gap and upper bound \kappa on its spectral ratio, our QAO algorithm returns m using \Gamma with probability (1-\epsilon)(1-e^{-1/\epsilon}) in time \widetilde{\mathcal{O}}(\epsilon ^{-1[\sqrt{V} + (\kappa-1)^{2/3}V^{2/3}]} ^{-1[\sqrt{|\mathcal{V}|} + (\kappa-1)^{2/3}|\mathcal{V}|^{2/3}]} ).
Edit intent: fluency
Original:  This achieves a quantum advantage for all \kappa, and when \kappa \approx 1, recovers Grover scaling up to logarithmic factors .
Revised:  This achieves a quantum advantage for all \kappa, and recovers Grover scaling up to logarithmic factors .
Edit intent: clarity
Original:  This achieves a quantum advantage for all \kappa, and when \kappa \approx 1, recovers Grover scaling up to logarithmic factors .
Revised:  This achieves a quantum advantage for all \kappa, and when \kappa \approx 1, recovers Grover scaling up to logarithmic factors when \kappa \approx 1.
Edit intent: clarity
Original:  We implement the algorithm as a subroutine in an optimization procedure that produces m with exponentially small failure probability and expected runtime \widetilde{\mathcal{O}}(\epsilon ^{-1[\sqrt{V} + (\kappa-1)^{2/3}V^{2/3}]) , } [\sqrt{|\mathcal{V}|} + (\kappa-1)^{2/3}|\mathcal{V}|^{2/3}]) } even when \kappa is not known beforehand.
Revised:  We implement the algorithm as a subroutine in an optimization procedure that produces m with exponentially small failure probability and expected runtime \widetilde{\mathcal{O}}(\epsilon [\sqrt{V} + (\kappa-1)^{2/3}V^{2/3}]) , } [\sqrt{|\mathcal{V}|} + (\kappa-1)^{2/3}|\mathcal{V}|^{2/3}]) } even when \kappa is not known beforehand.
Edit intent: coherence
Original:  We implement the algorithm as a subroutine in an optimization procedure that produces m with exponentially small failure probability and expected runtime \widetilde{\mathcal{O}}(\epsilon ^{-1[\sqrt{V} + (\kappa-1)^{2/3}V^{2/3}]) , } [\sqrt{|\mathcal{V}|} + (\kappa-1)^{2/3}|\mathcal{V}|^{2/3}]) } even when \kappa is not known beforehand.
Revised:  We implement the algorithm as a subroutine in an optimization procedure that produces m with exponentially small failure probability and expected runtime \widetilde{\mathcal{O}}(\epsilon ^{-1[\sqrt{V} + (\kappa-1)^{2/3}V^{2/3}]) , } ^{-1[\sqrt{|\mathcal{V}|} + (\kappa-1)^{2/3}|\mathcal{V}|^{2/3}]) } even when \kappa is not known beforehand.
Edit intent: fluency
Original:  The proposed technologies are based one a new Variational Principle which constructs a transformation with prescribed Jacobian determinant (which models local size changes) and prescribed curl-vector (which models local rotations).
Revised:  The proposed technologies are based on a new Variational Principle which constructs a transformation with prescribed Jacobian determinant (which models local size changes) and prescribed curl-vector (which models local rotations).
Edit intent: fluency
Original:  To address this challenging problem, we develop a dedicated neural network-based solution Hierarchical Attention based Food Recommendation (HAFR) which is capable of: 1) capturing the collaborative filtering effect like what similar users tend to eat;
Revised:  To address this challenging problem, we develop a dedicated neural network-based solution Hierarchical Attention based Food Recommendation (HAFR) which is capable of: 1) capturing the collaborative filtering effect like what similar users tend to eat;
Edit intent: fluency
Original:  Extensive experiments show that our method outperforms several competing recommender solutions like Factorization Machine and Visual Bayesian Personalized Ranking with an average improvement of 12 %DIFDELCMD < \\%%% %DIF < ,  offering promising results in predicting user preference on food.
Revised:  Extensive experiments show that our method outperforms several competing recommender solutions like Factorization Machine and Visual Bayesian Personalized Ranking with an average improvement of 12 %DIFDELCMD < \\%%% %DIF < , \%, offering promising results in predicting user preference on food.
Edit intent: fluency
Original:  Deciding what food to eat is a complex and multi-faceted process, which is influenced by many factors such as the ingredients, appearance of the recipe,  user's personal preference on food, and various contexts like what had been eaten in  past meals.
Revised:  Deciding what food to eat is a complex and multi-faceted process, which is influenced by many factors such as the ingredients, appearance of the recipe, the user's personal preference on food, and various contexts like what had been eaten in past meals.
Edit intent: fluency
Original:  Deciding what food to eat is a complex and multi-faceted process, which is influenced by many factors such as the ingredients, appearance of the recipe,  user's personal preference on food, and various contexts like what had been eaten in  past meals.
Revised:  Deciding what food to eat is a complex and multi-faceted process, which is influenced by many factors such as the ingredients, appearance of the recipe, user's personal preference on food, and various contexts like what had been eaten in the past meals.
Edit intent: fluency
Original:  To address this challenging problem, we develop a dedicated neural network-based solution Hierarchical Attention based Food Recommendation (HAFR) which is capable of: 1) capturing the collaborative filtering effect like what similar users tend to eat;
Revised:  To address this challenging problem, we develop a dedicated neural network based solution Hierarchical Attention based Food Recommendation (HAFR) which is capable of: 1) capturing the collaborative filtering effect like what similar users tend to eat;
Edit intent: fluency
Original:  and 3) learning user preference from the recipe's visual image .
Revised:  and 3) learning user preference from the recipe's visual images .
Edit intent: fluency
Original: Statistical physics is the natural framework to model complex networks.
Revised: In the last 15 years, statistical physics has been a very successful framework to model complex networks.
Edit intent: coherence
Original:  In the last twenty years, it has brought novel physical insights on a variety of emergent phenomena, such as self-organisation, scale invariance,  mixed distributions and ensemble non-equivalence, which cannot be deduced from the behaviour of the individual constituents .
Revised:  In the last twenty years, it has brought novel insights into a variety of emergent phenomena, such as self-organisation, scale invariance, mixed distributions and ensemble non-equivalence, which cannot be deduced from the behaviour of the individual constituents .
Edit intent: clarity
Original:  In the last twenty years, it has brought novel physical insights on a variety of emergent phenomena, such as self-organisation, scale invariance,  mixed distributions and ensemble non-equivalence, which cannot be deduced from the behaviour of the individual constituents .
Revised:  In the last twenty years, it has brought novel physical insights on a variety of physical phenomena, such as self-organisation, scale invariance, mixed distributions and ensemble non-equivalence, which cannot be deduced from the behaviour of the individual constituents .
Edit intent: clarity
Original:  In the last twenty years, it has brought novel physical insights on a variety of emergent phenomena, such as self-organisation, scale invariance,  mixed distributions and ensemble non-equivalence, which cannot be deduced from the behaviour of the individual constituents .
Revised:  In the last twenty years, it has brought novel physical insights on a variety of emergent phenomena, such as self-organisation, scale invariance, emergence of mixed distributions and ensemble non-equivalence, which cannot be deduced from the behaviour of the individual constituents .
Edit intent: clarity
Original:  At the same time, thanks to its deep connection with information theory, statistical physics and the principle of maximum entropy have led to the definition of null models  reproducing some features of empirical networks , but otherwise as random as possible.
Revised:  At the same time, thanks to their deep connection with information theory, statistical physics and the principle of maximum entropy have led to the definition of null models reproducing some features of empirical networks , but otherwise as random as possible.
Edit intent: fluency
Original:  At the same time, thanks to its deep connection with information theory, statistical physics and the principle of maximum entropy have led to the definition of null models  reproducing some features of empirical networks , but otherwise as random as possible.
Revised:  At the same time, thanks to its deep connection with information theory, statistical physics and the principle of maximum entropy have led to the definition of null models for networks reproducing some features of empirical networks , but otherwise as random as possible.
Edit intent: clarity
Original:  At the same time, thanks to its deep connection with information theory, statistical physics and the principle of maximum entropy have led to the definition of null models  reproducing some features of empirical networks , but otherwise as random as possible.
Revised:  At the same time, thanks to its deep connection with information theory, statistical physics and the principle of maximum entropy have led to the definition of null models reproducing some features of real-world systems , but otherwise as random as possible.
Edit intent: clarity
Original:  We review here the statistical physics approach for complex networks and the null models for the various physical problems , focusing in particular on the analytic frameworks reproducing the local features of the network .
Revised:  We review here the statistical physics approach and the various null models for the various physical problems , focusing in particular on the analytic frameworks reproducing the local features of the network .
Edit intent: clarity
Original:  We review here the statistical physics approach for complex networks and the null models for the various physical problems , focusing in particular on the analytic frameworks reproducing the local features of the network .
Revised:  We review here the statistical physics approach for complex networks and the null models for complex networks , focusing in particular on the analytic frameworks reproducing the local features of the network .
Edit intent: clarity
Original:  We further survey the statistical physics frameworks that reproduce more complex, semi-local network features using Markov chain Monte Carlo sampling, and the models of generalised network structures such as multiplex networks, interacting networks and simplicial complexes.
Revised:  We further survey the statistical physics models that reproduce more complex, semi-local network features using Markov chain Monte Carlo sampling, and the models of generalised network structures such as multiplex networks, interacting networks and simplicial complexes.
Edit intent: clarity
Original:  We further survey the statistical physics frameworks that reproduce more complex, semi-local network features using Markov chain Monte Carlo sampling, and the models of generalised network structures such as multiplex networks, interacting networks and simplicial complexes.
Revised:  We further survey the statistical physics frameworks that reproduce more complex, semi-local network features using Markov chain Monte Carlo sampling, as well as the models of generalised network structures such as multiplex networks, interacting networks and simplicial complexes.
Edit intent: coherence
Original: Seismic inversion and imaging are adjoint-based optimization problems that processes up to terabytes of data, regularly exceeding the memory capacity of available computers.
Revised: Seismic inversion and imaging are adjoint-based optimization problems that process up to terabytes of data, regularly exceeding the memory capacity of available computers.
Edit intent: fluency
Original:  In this paper  we combine compression and checkpointing for the first time to compute a realistic seismic inversion.
Revised:  In this paper , we combine compression and checkpointing for the first time to compute a realistic seismic inversion.
Edit intent: fluency
Original: L'Ecuyer & Simard's Big Crush statistical test suite has revealed statistical flaws in many popular random number generators including Marsaglia's XorShift generators.
Revised: L'Ecuyer & Simard's Big Crush statistical test suite has revealed statistical flaws in many popular random number generators including Marsaglia's Xorshift generators.
Edit intent: fluency
Original:  We examine the requirements of time protection, present a design and its implementation in the seL4 mircokernel , and evaluate its efficacy as well as performance overhead on Arm and x86 processors.
Revised:  We examine the requirements of time protection, present a design and its implementation in the seL4 microkernel , and evaluate its efficacy as well as performance overhead on Arm and x86 processors.
Edit intent: fluency
Original:  As demonstrated via numerical examples, these schemes prove effective in the atomic scaling as well as the semiclassical regime, and are a particularly appealing alternative to time-ordered exponential splittings when the laser potential is highly oscillatory or known only at specific points in time (on an equispaced grid, for instance).
Revised:  As demonstrated via numerical examples, these schemes prove effective in the atomic regime as well as the semiclassical regime, and are a particularly appealing alternative to time-ordered exponential splittings when the laser potential is highly oscillatory or known only at specific points in time (on an equispaced grid, for instance).
Edit intent: clarity
Original: This paperpresents a novel physics-informed regularization method for training of deep neural networks (DNNs)  .
Revised: In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) .
Edit intent: clarity
Original:  In particular, we focus on the DNN representation for the response of a physical or biological system, for which  a set of governing laws are known .
Revised:  In particular, we focus on prediction of a physical or biological system, for which a set of governing laws are known .
Edit intent: clarity
Original:  In particular, we focus on the DNN representation for the response of a physical or biological system, for which  a set of governing laws are known .
Revised:  In particular, we focus on the DNN representation for the response of a physical system, for which a set of governing laws are known .
Edit intent: clarity
Original:  In particular, we focus on the DNN representation for the response of a physical or biological system, for which  a set of governing laws are known .
Revised:  In particular, we focus on the DNN representation for the response of a physical or biological system, for which a set of governing laws is also available .
Edit intent: clarity
Original:  These laws often appear in the form of differential equations, derived from first principles, empirically-validated laws, and/ or domain expertise  .
Revised:  These laws often appear in the form of differential equations, derived from first principles, empirically-validated laws, or domain expertise .
Edit intent: fluency
Original:  We propose a DNN training approach that utilizes these known differential equations in addition to the measurement data, by introducing a penalty term to the training loss function to penalize divergence form the governing laws.
Revised:  We propose a training approach that utilizes these known differential equations in addition to the measurement data, by introducing a penalty term to the training loss function to penalize divergence form the governing laws.
Edit intent: clarity
Original:  Through three numerical examples , we will show that the proposed regularization produces surrogates that are physically interpretable with smaller generalization errors, when compared to other common regularization methods  .
Revised:  Through three numerical examples , we will show that the proposed regularization produces surrogates that are physically interpretable with smaller generalization errors, compared to other common regularization methods .
Edit intent: coherence
Original:  In this context, first, this article provides a clear overview of current multiagent deep reinforcement learning (MDRL) literature.
Revised:  The primary goal of this article is to provide a clear overview of current multiagent deep reinforcement learning (MDRL) literature.
Edit intent: clarity
Original:  Second, it provides guidelines to complement this emerging area by (i) showcasing examples on how methods and algorithms from DRL and multiagent learning (MAL) have helped solve problems in MDRL and (ii) providing general lessons learned from these works.
Revised:  Additionally, we complement the overview with a broader analysis: (i) showcasing examples on how methods and algorithms from DRL and multiagent learning (MAL) have helped solve problems in MDRL and (ii) providing general lessons learned from these works.
Edit intent: clarity
Original:  We expect this article will help unify and motivate future research to take advantage of the abundant literature that exists in both areas (DRL and MAL) in a joint effort to promote fruitful research in the multiagent community.
Revised:  We expect this article will help unify and motivate future research to take advantage of the abundant literature that exists (e.g., RL and MAL) in a joint effort to promote fruitful research in the multiagent community.
Edit intent: clarity
Original: The contribution of this paper is twofold: First, we prove existence and uniqueness of the weighted maximum likelihood estimator of the multivariate Student-t distribution and propose an efficient algorithm for its computation that we call generalized multivariate myriad filter (GMMF) . Second, we use the GMMF in a nonlocal framework for the denoising of images corrupted by different kinds of noise.
Revised: The contribution of this paper is twofold: First, we propose an efficient algorithm for the computation of the (weighted) maximum likelihood estimators for the parameters of the multivariate Student-t distribution and propose an efficient algorithm for its computation that we call generalized multivariate myriad filter (GMMF) . Second, we use the GMMF in a nonlocal framework for the denoising of images corrupted by different kinds of noise.
Edit intent: clarity
Original: The contribution of this paper is twofold: First, we prove existence and uniqueness of the weighted maximum likelihood estimator of the multivariate Student-t distribution and propose an efficient algorithm for its computation that we call generalized multivariate myriad filter (GMMF) . Second, we use the GMMF in a nonlocal framework for the denoising of images corrupted by different kinds of noise.
Revised: The contribution of this paper is twofold: First, we prove existence and uniqueness of the weighted maximum likelihood estimator of the multivariate Student-t distribution , which we call generalized multivariate myriad filter (GMMF) . Second, we use the GMMF in a nonlocal framework for the denoising of images corrupted by different kinds of noise.
Edit intent: clarity
Original: The contribution of this paper is twofold: First, we prove existence and uniqueness of the weighted maximum likelihood estimator of the multivariate Student-t distribution and propose an efficient algorithm for its computation that we call generalized multivariate myriad filter (GMMF) . Second, we use the GMMF in a nonlocal framework for the denoising of images corrupted by different kinds of noise.
Revised: The contribution of this paper is twofold: First, we prove existence and uniqueness of the weighted maximum likelihood estimator of the multivariate Student-t distribution and propose an efficient algorithm for its computation that we call generalized multivariate myriad filter . Second, we use the GMMF in a nonlocal framework for the denoising of images corrupted by different kinds of noise.
Edit intent: clarity
Original: The contribution of this paper is twofold: First, we prove existence and uniqueness of the weighted maximum likelihood estimator of the multivariate Student-t distribution and propose an efficient algorithm for its computation that we call generalized multivariate myriad filter (GMMF) . Second, we use the GMMF in a nonlocal framework for the denoising of images corrupted by different kinds of noise.
Revised: The contribution of this paper is twofold: First, we prove existence and uniqueness of the weighted maximum likelihood estimator of the multivariate Student-t distribution and propose an efficient algorithm for its computation that we call generalized multivariate myriad filter (GMMF) . Second, we use the generalized multivariate myriad filter in a nonlocal framework for the denoising of images corrupted by different kinds of noise.
Edit intent: coherence
Original:  The resulting method is very flexible and can handle very heavy-tailed noise such as Cauchy noise, but also also Gaussian or wrapped Cauchy noise  .
Revised:  The resulting method is very flexible and can handle heavy-tailed noise such as Cauchy noise, but also also Gaussian or wrapped Cauchy noise .
Edit intent: clarity
Original: The contribution of this paper is twofold: First, we propose an efficient algorithm for the computation of the (weighted) maximum likelihood estimators for the parameters of the multivariate Student-t distribution, which we call generalized multivariate myriad filter.
Revised: The contribution of this study is twofold: First, we propose an efficient algorithm for the computation of the (weighted) maximum likelihood estimators for the parameters of the multivariate Student-t distribution, which we call generalized multivariate myriad filter.
Edit intent: clarity
Original:  The resulting method is very flexible and can handle heavy-tailed noise such as Cauchy noise, but on the other extreme also Gaussian noiseis covered .
Revised:  The resulting method is very flexible and can handle heavy-tailed noise such as Cauchy noise, as well as the other extreme also Gaussian noiseis covered .
Edit intent: coherence
Original:  The resulting method is very flexible and can handle heavy-tailed noise such as Cauchy noise, but on the other extreme also Gaussian noiseis covered .
Revised:  The resulting method is very flexible and can handle heavy-tailed noise such as Cauchy noise, but on the other extreme , namely Gaussian noise .
Edit intent: clarity