wanyu/IteraTeR_v2 huggingface dataset:
Original:  We test them on over 30 real-life networks in 6 different disciplines (social, genetic, transport, co-authorship, trade  and neuronal networks).
Revised:  We test them on over 30 real-life networks in 6 different disciplines (social, genetic, transport, co-authorship, trade , and neuronal networks).
Edit intent: fluency
Original:  We further propose a random generator, displaying comparable patterns of elementary layer entanglement and transition layer entanglement across 1,329,696 synthetic coupled multilayer networks.
Revised:  We further propose a random generator, displaying comparable patterns of elementary layer entanglement and transition coupling entanglement across 1,329,696 synthetic coupled multilayer networks.
Edit intent: fluency
Original: Cross-impact, namely the fact that on average buy (sell) trades on a financial instrument induce positive (negative) price changes in other correlated assets, can be measured from abundant, although noisy, market data .
Revised: Trading a financial instrument induce positive (negative) price changes in other correlated assets, can be measured from abundant, although noisy, market data .
Edit intent: clarity
Original:  In this paper, we develop a new mixed model with preferences and hybrid transitions for the next-basket recommendation problem .
Revised:  In this paper, we develop a novel mixed model with preferences and hybrid transitions for the next-basket recommendation problem .
Edit intent: clarity
Original:  In this paper, we develop a new mixed model with preferences and hybrid transitions for the next-basket recommendation problem .
Revised:  In this paper, we develop a new mixed model with preferences and hybrid transitions for the next-basket recommendation .
Edit intent: clarity
Original:  This method explicitly models three important factors  : 1) users' general preferences ;
Revised:  This method explicitly models three important factors : 1) users' general preferences ,
Edit intent: fluency
Original:  2)  transition patterns among items and 3) transition patterns among baskets .
Revised:  2) transition patterns among items and 3) transition patterns among items .
Edit intent: clarity
Original:  We also conducted a comprehensive ablation study to verify the effectiveness of the different factors  .
Revised:  We also conducted a comprehensive ablation study to verify the effects of the different factors .
Edit intent: clarity
Original:  The motivation stems from practical demand to understand the tails of distributions, and hence for sketches to be more accurate near extreme values.
Revised:  The motivation stems from practical demands to understand the tails of distributions, and hence for sketches to be more accurate near extreme values.
Edit intent: fluency
Original:  This paper presents a randomized sketch of size O(\log^{1.
Revised:  This paper presents a randomized algorithm storing O(\log^{1.
Edit intent: clarity
Original:  Moreover, our sketch is fully mergeable, which makes it suitable for a parallel or distributed environment .
Revised:  Moreover, our sketch is fully mergeable, rendering it suitable for a parallel or distributed environment .
Edit intent: clarity
Original:  Moreover, our sketch is fully mergeable, which makes it suitable for a parallel or distributed environment .
Revised:  Moreover, our sketch is fully mergeable, which makes it suitable for parallel and distributed computing environments .
Edit intent: clarity
Original:  First, we derived the basic reproduction number, R_0  and estimated the effective reproduction R_{\rm eff} for each countries .
Revised:  First, we derived the basic reproduction number, R_0 , and estimated the effective reproduction R_{\rm eff} for each countries .
Edit intent: fluency
Original:  First, we derived the basic reproduction number, R_0  and estimated the effective reproduction R_{\rm eff} for each countries .
Revised:  First, we derived the basic reproduction number, R_0 and estimated the effective reproduction R_{\rm eff} for each country .
Edit intent: fluency
Original:  In this paper, we establish a mathematical foundation of the PINNs methodology.
Edit intent: coherence
Original:  This question is also related to the generalization of PINNs.
Edit intent: coherence
Original:  By adapting the Schuader approach , we show that the sequence of minimizers strongly converges to the PDE solution in L^2 . Furthermore, we show that if each minimizer satisfies the initial/boundary conditions, the convergence mode can be improved to H^1.
Revised:  By adapting the Schuader approach , we show that the sequence of minimizers strongly converges to the PDE solution in L^2 . Furthermore, we show that if each minimizer satisfies the initial/boundary conditions, the convergence mode becomes H^1.
Edit intent: clarity
Original:  To the best of our knowledge, this is the first theoretical work that shows the consistency of the PINNsmethodology .
Revised:  To the best of our knowledge, this is the first theoretical work that shows the consistency of PINNs .
Edit intent: clarity
Original:  Instead of \sigma-machine introduced recently by Cerbai%DIFDELCMD < {\it %%% et al. , we focus our study on (\sigma,\tau)-machine where the first stack avoids two patterns of length three, \sigma and \tau, and the second stack avoids the pattern 21.
Revised:  Instead of \sigma-machine introduced recently by Cerbai%DIFDELCMD < {\it %%% , we focus our study on (\sigma,\tau)-machine where the first stack avoids two patterns of length three, \sigma and \tau, and the second stack avoids the pattern 21.
Edit intent: coherence
Original:  Instead of \sigma-machine introduced recently by Cerbai%DIFDELCMD < {\it %%% et al. , we focus our study on (\sigma,\tau)-machine where the first stack avoids two patterns of length three, \sigma and \tau, and the second stack avoids the pattern 21.
Revised:  Instead of \sigma-machine introduced recently by Cerbai%DIFDELCMD < {\it %%% et al. , we focus our study on (\sigma,\tau)-machine where the first stack avoids a pair of patterns of length three, \sigma and \tau, and the second stack avoids the pattern 21.
Edit intent: clarity
Original: We provide a data-driven analysis of how investor expectations about economic growth and stock market returns changed during the February-March 2020 stock market crash induced by the COVID-19 pandemic  .
Revised: We analyze how investor expectations about economic growth and stock market returns changed during the February-March 2020 stock market crash induced by the COVID-19 pandemic .
Edit intent: clarity
Original: We provide a data-driven analysis of how investor expectations about economic growth and stock market returns changed during the February-March 2020 stock market crash induced by the COVID-19 pandemic  .
Revised: We provide a data-driven analysis of how investor expectations about economic growth and stock returns changed during the February-March 2020 stock market crash induced by the COVID-19 pandemic .
Edit intent: fluency
Original:  The \\%DIF > , and \\%DIF > from its lowest point.  average investor turned more pessimistic about the short-run performance of both stock markets and the economy.
Revised:  The \\%DIF > , and \\%DIF > from its lowest point. average investor turned more pessimistic about the short-run performance of both the stock market and the real economy.
Edit intent: clarity
Original:  Investors also perceived higher probability of both further extreme stock market declines and large declines in short-run real economic activity.
Revised:  Investors also perceived higher probabilities of both further extreme stock market declines and large declines in short-run real economic activity.
Edit intent: fluency
Original:  In contrast, investors' expectations about the long run remained largely unchanged, and if anything improved.
Revised:  In contrast, investors' expectations about the long run remained largely unchanged, and , if anything, improved.
Edit intent: fluency
Original:  Today's systems typically implement one analysis/platform combination, requiring data scientists to constantly switch tools and duplicating implementation effort over many data science libraries .
Revised:  Today's systems typically implement one analysis/platform combination, leading to repeated implementation effort -- and a plethora of semi-compatible tools for data scientists .
Edit intent: clarity
Original:  In this paper, we propose the "Collection Virtual Machine" (or CVM) -- an abstraction that can capture the essence of a large span of  types of analyses and backend implementations .
Revised:  In this paper, we propose the "Collection Virtual Machine" (or CVM) -- an abstraction that can capture the essence of a large span of types of analyses .
Edit intent: coherence
Original:  While reducing the overall implementation effort, we also improve interoperability of both analyses and hardware platforms.
Revised:  While reducing the overall implementation effort, this also improves the interoperability of both analyses and hardware platforms.
Edit intent: coherence
Original:  Our findings show that, for one of H3's early implementations, H3 is consistently worse than H2 in terms of performance.
Revised:  Our findings show that, for one of H3's early implementations, H3 is mostly worse but achieves a higher average throughput
Edit intent: clarity
Original:  Through boundary integral equations and shape derivatives, the profile of a grating (taken to be a perfect electric conductor) is optimized such that it maximizes the diffraction efficiency for a given diffraction mode .
Revised:  Through boundary integral equations and shape derivatives, the profile of a grating is optimized such that it maximizes the diffraction efficiency for a given diffraction mode .
Edit intent: clarity
Original:  We provide a thorough comparison of two optimization methods: a first-order one based on gradient descentand a second-order approach based on Newton iteration.
Revised:  We provide a thorough comparison of two optimization methods: a first-order method (gradient descent); a second-order approach based on Newton iteration.
Edit intent: clarity
Original:   While we introduce and propose such notions in a general setting,  we only work out the case of planar graphs.
Revised:  While we introduce and propose these notions in a general setting, we only work out the case of planar graphs.
Edit intent: fluency
Original:   While we introduce and propose such notions in a general setting,  we only work out the case of planar graphs.
Revised:  While we introduce and propose such notions in a general setting, in this paper, we only work out the case of planar graphs.
Edit intent: clarity
Original:  Specifically, we explain that circulation depends on a scalar potential in a manner that is similar to the curl of planar vector fields.
Revised:  We explain that a scalar potential in a manner that is similar to the curl of planar vector fields.
Edit intent: clarity
Original:  For general graphs, assessing global circulation remains at present a combinatorial problem.
Revised:  Beyond planar graphs, in the general case, the problem to determine global circulation remains at present a combinatorial problem.
Edit intent: clarity
Original: In a subjective experiment to evaluate the perceptual audiovisual quality of multimedia and television services, raw opinion scores offered by subjects are often noisy and unreliable.
Revised: In a subjective experiment to evaluate the perceptual audiovisual quality of multimedia and television services, raw opinion scores collected from test subjects are often noisy and unreliable.
Edit intent: clarity
Original:  Recommendations such as ITU-R BT.500, ITU-T P.910 and ITU-T P.913 standardize post-processing procedures to clean up the raw opinion scores, using techniques such as subject outlier rejection and bias removal.
Revised:  Recommendations such as ITU-R BT.500, ITU-T P.910 and ITU-T P.913 standardize post-test screening procedures to clean up the raw opinion scores, using techniques such as subject outlier rejection and bias removal.
Edit intent: clarity
Original:  As an alternative, we propose a simple model to account for two of the most dominant behaviors of subject inaccuracy: bias (aka systematic error) and inconsistency(aka random error) .
Revised:  As an alternative, we propose a simple model to account for two of the most dominant behaviors of subject inaccuracy: bias and inconsistency .
Edit intent: clarity
Original:  We propose to use maximum likelihood estimation (MLE) to jointly estimate the model parameters, and present two numeric solvers: the first based on the Newton-Raphson method, and the second based on alternating projection .
Revised:  We propose to use maximum likelihood estimation to jointly solve the model parameters, and present two numeric solvers: the first based on the Newton-Raphson method, and the second based on alternating projection .
Edit intent: clarity
Original:  We propose to use maximum likelihood estimation (MLE) to jointly estimate the model parameters, and present two numeric solvers: the first based on the Newton-Raphson method, and the second based on alternating projection .
Revised:  We propose to use maximum likelihood estimation (MLE) to jointly estimate the model parameters, and present two numeric solvers: the first based on the Newton-Raphson method, and the second based on an alternating projection (AP) .
Edit intent: clarity
Original:  We show that the second solver can be considered as a generalization of the subject bias removal procedure in ITU-T P.913  . We compare the proposed methods with the standardized techniques using real datasets and synthetic simulations,
Revised:  We show that the AP solver generalizes the ITU-T P.913 . We compare the proposed methods with the standardized techniques using real datasets and synthetic simulations,
Edit intent: clarity
Original:  and demonstrate that the proposed methods have advantages in better model-data fit, tighter confidence intervals, better robustness against subject outliers, shorter runtime, the absence of hard coded parameters and thresholds, and auxiliary information on test subjects.
Revised:  and demonstrate that the proposed methods have advantages in better model-data fit, tighter confidence intervals, better robustness against subject outliers, the absence of hard coded parameters and thresholds, and auxiliary information on test subjects.
Edit intent: clarity
Original:  The source code for this work is open-sourced at URL
Revised:  The code for this work is open-sourced at URL
Edit intent: clarity
Original:   We show that zero queueing delay for such parallel jobs can be achieved using  a variant of the %DIFDELCMD < \pod%%% \ policy, the batch-filling policy, with a probe overhead d = \omega\left(1{(1-\lambda)\log k}\right)  , where k is the number of tasks in each job  .
Revised:  We show that zero queueing delay for parallel jobs can be achieved using a variant of the %DIFDELCMD < \pod%%% \ policy, the batch-filling policy, with a probe overhead d = \omega\left(1{(1-\lambda)\log k}\right) , where k is the number of tasks in each job .
Edit intent: clarity
Original:   We show that zero queueing delay for such parallel jobs can be achieved using  a variant of the %DIFDELCMD < \pod%%% \ policy, the batch-filling policy, with a probe overhead d = \omega\left(1{(1-\lambda)\log k}\right)  , where k is the number of tasks in each job  .
Revised:  We show that zero queueing delay for such parallel jobs can be achieved using the batch-filling policy ( a variant of the %DIFDELCMD < \pod%%% \ policy, the batch-filling policy, with a probe overhead d = \omega\left(1{(1-\lambda)\log k}\right) , where k is the number of tasks in each job .
Edit intent: fluency
Original:   We show that zero queueing delay for such parallel jobs can be achieved using  a variant of the %DIFDELCMD < \pod%%% \ policy, the batch-filling policy, with a probe overhead d = \omega\left(1{(1-\lambda)\log k}\right)  , where k is the number of tasks in each job  .
Revised:  We show that zero queueing delay for such parallel jobs can be achieved using a variant of the %DIFDELCMD < \pod%%% celebrated pod policy) with a probe overhead d = \omega\left(1{(1-\lambda)\log k}\right) , where k is the number of tasks in each job .
Edit intent: clarity
Original:  We report that Tau depletion in neuroblastoma cells severely dysregulate P53 activity and leads to reduced cell death counterbalanced by increased cell senescence.
Revised:  We report that Tau depletion in neuroblastoma cells severely dysregulate P53 activity and leads to reduced cell death and increased cell senescence.
Edit intent: clarity
Original:  As a consequence of DNA damage, abnormal modifications of both P53 and  MDM2 were detected in Tau-KO cells suggesting an important role of Tau in the regulation of P53 modification, stability and activity .
Revised:  As a consequence of DNA damage, abnormal modifications of both P53 and MDM2 .
Edit intent: clarity
Original:  Considering the medical need with vast social implications caused by neurodegenerative tauopathies and cancer, our study may lead to innovative approaches for disease-modifying therapies.
Revised:  Considering the medical need with vast social implications caused by neurodegeneration and cancer, our study may lead to innovative approaches for disease-modifying therapies.
Edit intent: clarity
Original:  Considering the medical need with vast social implications caused by neurodegenerative tauopathies and cancer, our study may lead to innovative approaches for disease-modifying therapies.
Revised:  Considering the medical need with vast social implications caused by neurodegenerative tauopathies and cancer, our study may reform our approach to disease-modifying therapies.
Edit intent: clarity
Original:  A numerical example shows that the model can be accurately calibrated to the SPX European optionsand the VIX futures simultaneously.
Revised:  A numerical example shows that the model can be accurately calibrated to SPX options, VIX options and VIX futures simultaneously.
Edit intent: clarity
Original:  But the main focusis on proving that the bounds are best possible.
Revised:  The main focus, however, is to prove that the bounds are best possible.
Edit intent: coherence
Original:  The paper is based on univariate results in (Goebbels, S .: On sharpness of error bounds for univariate approximation by single hidden layer feedforward neural networks.
Revised:  The paper is based on univariate results in (Goebbels, St .: On sharpness of error bounds for univariate approximation by single hidden layer feedforward neural networks.
Edit intent: fluency
Original: In this paper we propose regularized asymptotic descent (RAD) methods for solving nonconvex optimization problems.
Revised: We propose and analyze regularized asymptotic descent (RAD) methods for solving nonconvex optimization problems.
Edit intent: clarity
Original:  We consider a class of possibly nonconvex, nonsmooth, or even discontinuous objectives extended from strongly convex functions with Lipschitz-continuous gradients , in each of which has a unique global minima and is continuously differentiable at the global minimizer .
Revised:  We consider a class of possibly nonconvex, nonsmooth, or even discontinuous functions. Such functions are extended from strongly convex functions with Lipschitz-continuous gradients , in each of which has a unique global minima and is continuously differentiable at the global minimizer .
Edit intent: clarity
Original:  The main theoretical result shows that the RAD method enjoys the global linear convergence with high probability for such a class of nonconvex objectives, i. e., the method will not be trapped in saddle points, local minima, or even discontinuities.
Revised:  The main theoretical result shows that the method enjoys the global linear convergence with high probability for such a class of nonconvex objectives, i. e., the method will not be trapped in saddle points, local minima, or even discontinuities.
Edit intent: clarity
Original:  The main theoretical result shows that the RAD method enjoys the global linear convergence with high probability for such a class of nonconvex objectives, i. e., the method will not be trapped in saddle points, local minima, or even discontinuities.
Revised:  The main theoretical result shows that the RAD method enjoys the global linear convergence with high probability for such functions.
Edit intent: clarity
Original:  Besides, the method is derivative-free and its per-iteration cost, i.e., the number of function evaluations, is bounded, so that it has a complexity bound O(\log1{\epsilon}) for finding a point such that the optimality gap at this point is less than \epsilon>0. 
Revised:  Besides, the method is derivative-free and its per-iteration cost, i.e., the number of function evaluations, is bounded, so it has a complexity bound O(\log1{\epsilon}) for finding a point such that the optimality gap at this point is less than \epsilon>0. 
Edit intent: fluency
Original: We propose and analyze regularized asymptotic descent (RAD) methods for finding the global minimizer of a class of possibly nonconvex, nonsmooth, or even discontinuous functions.
Revised: We propose and analyze regularized asymptotic descent (RAD) methods to find the global minimizer of a class of possibly nonconvex, nonsmooth, or even discontinuous functions.
Edit intent: fluency
Original: We propose and analyze regularized asymptotic descent (RAD) methods for finding the global minimizer of a class of possibly nonconvex, nonsmooth, or even discontinuous functions.
Revised: We propose and analyze regularized asymptotic descent (RAD) methods for finding the global minimizer for a class of possibly nonconvex, nonsmooth, or even discontinuous functions.
Edit intent: clarity
Original: We propose and analyze regularized asymptotic descent (RAD) methods for finding the global minimizer of a class of possibly nonconvex, nonsmooth, or even discontinuous functions.
Revised: We propose and analyze regularized asymptotic descent (RAD) methods for finding the global minimizer of a class of nonconvex, nonsmooth, or even discontinuous functions.
Edit intent: clarity
Original:  Besides , the method is derivative-free and its per-iteration cost, i.e., the number of function evaluations, is  bounded, so it has a complexity bound O(\log1{\epsilon}) for finding a point such that the optimality gap at this point is less than \epsilon>0.
Revised:  Besides , the method is derivative-free and its per-iteration cost, i.e., the number of function evaluations, is also bounded, so it has a complexity bound O(\log1{\epsilon}) for finding a point such that the optimality gap at this point is less than \epsilon>0.
Edit intent: coherence
Original:  Numerical experiments in up to 500 dimensions demonstrate the benefits of the method.
Revised:  Numerical experiments in up to 500 demonstrate the benefits of the method.
Edit intent: clarity
Original:  In this paper, we significantly improve this result and show that the tandem duplication "distance problem " is NP-hard already for the case of strings over an alphabet of size \leq 5.
Revised:  In this paper, we significantly improve this result and show that the tandem duplication distance problem is NP-hard already for the case of strings over an alphabet of size \leq 5.
Edit intent: fluency
Original:  A polynomial time algorithm that solves this (existence ) problem was only known for the case of the binary alphabet .
Revised:  A polynomial time algorithm that solves the existence problem was only known for the case of the binary alphabet .
Edit intent: clarity
Original:  Recently, some authors started calling it "Christofides-Serdyukov algorithm", pointing out that the same result was published independently in the USSR in 1978.
Revised:  Recently, some authors started calling it "Christofides-Serdyukov algorithm", pointing out that it was published independently in the USSR in 1978.
Edit intent: clarity
Original:  We provide a detailed characterization of the learning performance by means of a steady-state analysis.
Revised:  First, we provide a detailed characterization of the learning performance by means of a steady-state analysis.
Edit intent: fluency