wanyu/IteraTeR_v2 huggingface dataset:
Original:  We prove that the algorithm recovers the tensor with maximum entry-wise error  and mean-squared-error (MSE) decaying to 0 as long as each entry is observed independently with probability p = \Omega(n^{-3/2 + \kappa}) for any arbitrarily small \kappa > 0. {\sf  {\sf   Our analysis sheds insight into the conjectured sample complexity lower bound, showing that it matches the connectivity threshold of the graph used by our algorithm for estimating similarity between coordinates.
Revised:  We prove that the algorithm recovers the tensor with maximum entry-wise error and mean-squared-error (MSE) decaying to 0 as long as each entry is observed independently with probability p = \Omega(n^{-3/2 + \kappa}) for any arbitrarily small \kappa > 0. {\sf poly {\sf Our analysis sheds insight into the conjectured sample complexity lower bound, showing that it matches the connectivity threshold of the graph used by our algorithm for estimating similarity between coordinates.
Edit intent: fluency
Original:  We prove that the algorithm recovers the tensor with maximum entry-wise error  and mean-squared-error (MSE) decaying to 0 as long as each entry is observed independently with probability p = \Omega(n^{-3/2 + \kappa}) for any arbitrarily small \kappa > 0. {\sf  {\sf   Our analysis sheds insight into the conjectured sample complexity lower bound, showing that it matches the connectivity threshold of the graph used by our algorithm for estimating similarity between coordinates.
Revised:  We prove that the algorithm recovers the tensor with maximum entry-wise error and mean-squared-error (MSE) decaying to 0 as long as each entry is observed independently with probability p = \Omega(n^{-3/2 + \kappa}) for any arbitrarily small \kappa > 0. {\sf {\sf poly Our analysis sheds insight into the conjectured sample complexity lower bound, showing that it matches the connectivity threshold of the graph used by our algorithm for estimating similarity between coordinates.
Edit intent: fluency
Original:  In general, least-squares approximations can be inaccurate and ill conditioned when the number of sample points M is close to N = \dim(P).
Revised:  In general, least-squares approximations can be inaccurate and ill-conditioned when the number of sample points M is close to N = \dim(P).
Edit intent: fluency
Original:  To counteract this, we introduce a novel method for sampling in general domains which leads to provably accurate and well-conditioned weighted least-squares approximations.
Revised:  To counteract this, we introduce a novel method for sampling in general domains which leads to provably accurate and well-conditioned approximations.
Edit intent: clarity
Original:  Our main result shows near optimal sample complexity for this procedure;
Revised:  Our main result shows near-optimal sample complexity for this procedure;
Edit intent: fluency
Original:  specifically, M = O(N \log(N)) samples suffice for a well conditioned and accurate approximation.
Revised:  specifically, M = O(N \log(N)) samples suffice for a well-conditioned and accurate approximation.
Edit intent: fluency
Original:  For the stochastic HNN, we show that the so-called `` diffusion machine", while not a gradient flow itself, induces a gradient flow when lifted in the space of probability measures.
Revised:  For the stochastic HNN, we show that the so-called " diffusion machine", while not a gradient flow itself, induces a gradient flow when lifted in the space of probability measures.
Edit intent: fluency
Original:  In this way, we are able to keep the computational cost and the storage significantly below more straightforward approaches.
Revised:  In this way, we are able to keep the computational cost and the storage requirements significantly below existing approaches.
Edit intent: clarity
Original:  These features allow us to perform reliable numerical simulations for longer times even in cases when the solution becomes highly oscillatory or seems to develop finite time blow-up.
Revised:  These features allow us to perform reliable numerical simulations for longer times even in cases where the solution becomes highly oscillatory or seems to develop finite time blow-up.
Edit intent: fluency
Original: The evolution of MobileNets has laid a solid foundation for neural network application on the mobile end.
Revised: The evolution of MobileNets has laid a solid foundation for neural network applications on mobile end.
Edit intent: fluency
Original:  With the latest MobileNetV3, neural architecture search again claimed its supremacy on network design.
Revised:  With the latest MobileNetV3, neural architecture search again claimed its supremacy in network design.
Edit intent: clarity
Original:  Till today all mobile methods mainly focus on CPU latency instead of GPU, the latter, however, has lower overhead and interference and is much preferred in the industry.
Revised:  Unfortunately, till today all mobile methods mainly focus on CPU latency instead of GPU, the latter, however, has lower overhead and interference and is much preferred in the industry.
Edit intent: coherence
Original:  Till today all mobile methods mainly focus on CPU latency instead of GPU, the latter, however, has lower overhead and interference and is much preferred in the industry.
Revised:  Till today all mobile methods mainly focus on CPU latencies instead of GPU, the latter, however, has lower overhead and interference and is much preferred in the industry.
Edit intent: fluency
Original:  While urging higher capability and restraining time consumption , we unconventionally encourage increasing the number of parameters for higher representational power.
Revised:  Urging higher capability while restraining time consumption , we unconventionally encourage increasing the number of parameters for higher representational power.
Edit intent: coherence
Original:  In both cases we use techniques developed for computing the sum of the distances, which does not have ``inverse'' component, together with batched evaluations of rational functions.
Revised:  In both cases we use techniques developed for computing the sum of the distances, which does not have "inverse" component, together with batched evaluations of rational functions.
Edit intent: fluency
Original:  The objective function is the sum of a multi-block relatively smooth function (i.e., relatively smooth by fixing all the blocks except one \mbox{ bauschke2016descent,lu2018relatively ) and block separable (nonsmooth) nonconvex functions.
Revised:  The objective function is the sum of a multi-block relatively smooth function (i.e., relatively smooth by fixing all the blocks except one ) and block separable (nonsmooth) nonconvex functions.
Edit intent: coherence
Original:  The rate of convergence is further analyzed for functions satisfying the {\L}ojasiewicz's gradient inequality.
Revised:  Further, the rate of convergence is further analyzed for functions satisfying the {\L}ojasiewicz's gradient inequality.
Edit intent: coherence
Original:  We apply this framework to orthogonal nonnegative matrix factorization (ONMF) and sparse ONMF (SONMF) that both satisfy all of our assumptions and the related subproblems are solved in closed forms  .
Revised:  We apply this framework to orthogonal nonnegative matrix factorization (ONMF) that satisfies all of our assumptions and the related subproblems are solved in closed forms .
Edit intent: clarity
Original:  To deal with the issue fundamentally, we incorporate macro actions , defined as sequences of primitive actions, into the primitive action space to form an augmented action space.
Revised:  To deal with the issue fundamentally, we incorporate macro actions , defined as a sequence of primitive actions, into the primitive action space to form an augmented action space.
Edit intent: fluency
Original:  The agent using a proper augmented action space is able to jump to a farther state and thus speed up the exploration process as well as facilitate the learning procedure.
Revised:  The agent using a proper augmented action space is able to bypass intermediate states to a farther state and thus speed up the exploration process as well as facilitate the learning procedure.
Edit intent: clarity
Original:  The agent using a proper augmented action space is able to jump to a farther state and thus speed up the exploration process as well as facilitate the learning procedure.
Revised:  The agent using a proper augmented action space is able to jump to a farther state and facilitate its learning procedure.
Edit intent: clarity
Original:  We conduct a detailed complexity analysis and show that indices defined with FLuID can be efficiently computed on average in \Theta(n ) w.r.t. n being the number of triples in the input data graph.
Revised:  We conduct a detailed complexity analysis and show that indices defined with FLuID can be efficiently computed on average in \Theta(n ) w.r.t. n the number of triples in the input data graph.
Edit intent: clarity
Original:  We conduct a detailed complexity analysis and show that indices defined with FLuID can be efficiently computed on average in \Theta(n ) w.r.t. n being the number of triples in the input data graph.
Revised:  We conduct a detailed complexity analysis and show that indices defined with FLuID can be efficiently computed on average in \Theta(n ) w.r.t. n being the number of edges in the data graph.
Edit intent: clarity
Original: Summarization is a widespread method to handle very large graphs.
Revised: Summarization is a widespread method for handling very large graphs.
Edit intent: fluency
Original:  The task of structural graph summarization is to compute a concise while at the same time meaningful synopsis of the key structural information of the graph.
Revised:  The task of structural graph summarization is to compute a concise but meaningful synopsis of the key structural information of the graph.
Edit intent: coherence
Original:  The task of structural graph summarization is to compute a concise while at the same time meaningful synopsis of the key structural information of the graph.
Revised:  The task of structural graph summarization is to compute a concise while at the same time meaningful synopsis of the key structural information of a graph.
Edit intent: fluency
Original:  As there are many tasks regarding what information is to be summarized from a graph , there is no single concept or model of graph summaries.
Revised:  As summaries may be used for many different purposes , there is no single concept or model of graph summaries.
Edit intent: clarity
Original:  We have studied existing structural graph summaries for large (semantic) graphs.
Revised:  We have studied existing structural graph summaries for large-scale (semantic) graphs.
Edit intent: clarity
Original:  Despite the different purposes and concepts followed by the existing graph summaries , we found common patterns in the captured graph structures .
Revised:  Despite their different concepts and purposes , we found common patterns in the captured graph structures .
Edit intent: clarity
Original:  We abstract from these patterns and provide for the first time a formally defined common model  FLUID (FLexible graph sUmmarIes for Data graphs) that allows to flexibly define structural graph summaries.
Revised:  We abstract from these patterns and provide for the first time a formally defined common model , FLUID (FLexible graph sUmmarIes for Data graphs) that allows to flexibly define structural graph summaries.
Edit intent: fluency
Original:  We abstract from these patterns and provide for the first time a formally defined common model  FLUID (FLexible graph sUmmarIes for Data graphs) that allows to flexibly define structural graph summaries.
Revised:  We abstract from these patterns and provide for the first time a formally defined common model FLUID (FLexible graph sUmmarIes for Data graphs) , that allows us to flexibly define structural graph summaries.
Edit intent: fluency
Original:  FLUID allows to quickly define, adapt, and compare different graph summaries for different purposes and datasets.
Revised:  FLUID allows graph summaries to be quickly defined, adapted, and compared for different purposes and datasets.
Edit intent: clarity
Original:  We show that graph summaries defined with FLUID can be computed in the worst case in  O(n^2) w.r.t. n  the number of edges in the data graph.
Revised:  We show that graph summaries defined with FLUID can be computed in the worst case in time O(n^2) w.r.t. n the number of edges in the data graph.
Edit intent: clarity
Original:  We show that graph summaries defined with FLUID can be computed in the worst case in  O(n^2) w.r.t. n  the number of edges in the data graph.
Revised:  We show that graph summaries defined with FLUID can be computed in the worst case in O(n^2) w.r.t. n , the number of edges in the data graph.
Edit intent: fluency
Original:  However, we analyzed large-scale graphs obtained from the web with billions of edges and found indications that the average complexity is bounded by \Theta(n).
Revised:  An empirical analysis of large-scale graphs obtained from the web with billions of edges and found indications that the average complexity is bounded by \Theta(n).
Edit intent: clarity
Original:  However, we analyzed large-scale graphs obtained from the web with billions of edges and found indications that the average complexity is bounded by \Theta(n).
Revised:  However, we analyzed large-scale web graphs with billions of edges and found indications that the average complexity is bounded by \Theta(n).
Edit intent: clarity
Original:  However, we analyzed large-scale graphs obtained from the web with billions of edges and found indications that the average complexity is bounded by \Theta(n).
Revised:  However, we analyzed large-scale graphs obtained from the web with billions of edges indicates a typical running time of \Theta(n).
Edit intent: clarity
Original:  Finally, we provide a formal declarative language for FLUID , which allows application developers to quickly define and modify their graph summaries.
Revised:  Based on the formal FLUID model, one can quickly define and modify their graph summaries.
Edit intent: clarity
Original:  The language can be used to build any of the existing structural graph summaries found in the literature and beyond .
Revised:  The language can be used to build any of the existing structural graph summaries from the literature and beyond .
Edit intent: clarity
Original: A tensor decomposition approach for the solution of high-dimensional, fully nonlinear Hamilton-Jacobi-Bellman equations arising in optimal feedback control and estimation of nonlinear dynamics is presented.
Revised: A tensor decomposition approach for the solution of high-dimensional, fully nonlinear Hamilton-Jacobi-Bellman equations arising in optimal feedback control of nonlinear dynamics is presented.
Edit intent: clarity
Original:  The proposed method combines a tensor train approximation for the value function together with a Newton-like iterative method for the solution of the resulting nonlinear system.
Revised:  The method combines a tensor train approximation for the value function together with a Newton-like iterative method for the solution of the resulting nonlinear system.
Edit intent: clarity
Original:  Numerical tests including the control of a 2D nonlinear reaction equation and the stabilization of a bilinear Fokker-Planck equation are presented .
Revised:  Numerical tests including the control of a 2D nonlinear reaction equation and the stabilization of a bilinear Fokker-Planck equations .
Edit intent: clarity
Original:  We present numerical results for a large number of example problems, which include the pricing of many high-dimensional American and Bermudan options such as, for example, Bermudan max-call options in up to 5000 ~ dimensions.
Revised:  We present numerical results for a large number of example problems, which include the pricing of many high-dimensional American and Bermudan options such as, for example, Bermudan max-call options in up to 5000 dimensions.
Edit intent: fluency
Original: Nowadays many financial derivatives which are traded on stock and futures exchanges , such as American or Bermudan options, are of early exercise type.
Revised: Nowadays many financial derivatives , such as American or Bermudan options, are of early exercise type.
Edit intent: clarity
Original:  Often the pricing of early exercise options gives rise to high-dimensional optimal stopping problems, since the dimension corresponds to the number of underlyings in the associated hedging portfolio .
Revised:  Often the pricing of early exercise options gives rise to high-dimensional optimal stopping problems, since the dimension corresponds to the number of underlying assets .
Edit intent: clarity
Original:  In this work  we propose an algorithm for solving such problems, which is based on deep learning and computes, in the context of early exercise option pricing, both approximations for an optimal exercise strategy and the price of the considered option.
Revised:  In this work , we propose an algorithm for solving such problems, which is based on deep learning and computes, in the context of early exercise option pricing, both approximations for an optimal exercise strategy and the price of the considered option.
Edit intent: fluency
Original:  In this work  we propose an algorithm for solving such problems, which is based on deep learning and computes, in the context of early exercise option pricing, both approximations for an optimal exercise strategy and the price of the considered option.
Revised:  In this work we propose an algorithm for solving such problems, which is based on deep learning and computes, in the context of early exercise option pricing, both approximations of an optimal exercise strategy and the price of the considered option.
Edit intent: fluency
Original:  We present numerical results for a large number of example problems, which include the pricing of many high-dimensional American and Bermudan options such as, for example, Bermudan max-call options in up to 5000 dimensions.
Revised:  We present numerical results for a large number of example problems, which include the pricing of many high-dimensional American and Bermudan options , such as Bermudan max-call options in up to 5000 dimensions.
Edit intent: coherence
Original:  Both methods can easily be applied to  problems with common noise, which is not the case with the existing technology.
Revised:  Both methods can easily be applied to certain problems with common noise, which is not the case with the existing technology.
Edit intent: clarity
Original:  Starting from a mean-field model where we describe AF as a simple birth-death process, we add layers of complexity to the model and show that persistent AF arises from the formation of temporally stable structural re-entrant circuits that form from the interaction of wavefront collisions during paroxysmal AF.
Revised:  Starting from a mean-field model where we describe AF as a simple birth-death process, we add layers of complexity to the model and show that persistent AF arises from re-entrant circuits that form from the interaction of wavefront collisions during paroxysmal AF.
Edit intent: clarity
Original:  Across such practices there is a variety of  instrumentation utilised.
Revised:  Across such practices there is a variety of acoustic instrumentation utilised.
Edit intent: clarity
Original:  Practitioners suggest the ability of sound to target both mental and even physical health issues, e.g., chronic-stress, or joint-pain.
Revised:  Practitioners suggest that sound has the ability to target both mental and even physical health issues, e.g., chronic-stress, or joint-pain.
Edit intent: clarity
Original:  Instruments including the Tibetan singing bowl and vocal chanting, are methods which are still widely encouraged today.
Revised:  Instruments including the Tibetan singing bowl and vocal chanting, are still widely used today.
Edit intent: clarity
Original:  With the noise-floor of modern urban soundscapes continually increasing and known to impact wellbeing, methods to approve daily soundscapes are needed.
Revised:  With the noise-floor of modern urban soundscapes continually increasing and known to impact wellbeing, methods to improve this are needed.
Edit intent: clarity
Original:  With this in mind, this study presents the Acoustic Sounds for Wellbeing (ASW) dataset.
Revised:  With that in mind, this study presents the Acoustic Sounds for Wellbeing (ASW) dataset.
Edit intent: fluency
Original:  The ASW dataset is a dataset gathered from YouTube including 88  + hrs of audio from 5-classes of acoustic instrumentation ( Chimes, Chanting, Drumming, Gongs, and Singing Bowl ).
Revised:  The ASW dataset is a dataset gathered from YouTube including 88 + hrs of audio from 5-classes of acoustic instrumentation ( Gongs, Drumming, Singing Bowls, and Chanting ).
Edit intent: clarity
Original:  We additionally present initial baseline classification results on the dataset, finding that conventional Mel-Frequency Cepstra coefficient features achieve at best an unweighted average recalled of 57.4 %DIFDELCMD < \\%%% %DIF < for a 5-class support vector machine classification task .
Revised:  We additionally present initial baseline classification results on the dataset, finding that conventional Mel-Frequency Cepstra coefficient features achieve at best an unweighted average recalled of 57.4 %DIFDELCMD < \\%%% %DIF < for a 5-class support vector machine \% for a 5-class support vector machine classification paradigm .
Edit intent: clarity
Original:  The new approach is well suited for implementation on CPUs and GPUs.
Revised:  This approach is well suited for implementation on CPUs and GPUs.
Edit intent: clarity
Original:  The method is matrix-free and uses an iterative formulation to setup and solve the pressure Poisson equation.
Revised:  The method is matrix-free and uses an iterative formulation to setup and solve the pressure-Poisson equation.
Edit intent: fluency
Original:  The new formulation enables the use of solid wall boundary conditions from the weakly-compressible SPH schemes.
Revised:  This formulation enables the use of solid wall boundary conditions from the weakly-compressible SPH schemes.
Edit intent: clarity
Original:  The new method is fast and runs on GPUs without the need for complex integration with sparse linear solvers  . Several benchmark problems that illustrate the robustness, performance, and wide range of applicability of the new scheme are demonstrated.
Revised:  The method is fast and runs on GPUs without the need for complex integration with sparse linear solvers . Several benchmark problems that illustrate the robustness, performance, and wide range of applicability of the new scheme are demonstrated.
Edit intent: coherence
Original: We present a general purpose method for solving partial differential equations on a closed surface, using a technique for discretizing the surface introduced by Wenjun Ying and Wei-Cheng Wang ( J. Comput.
Revised: We present a general purpose method for solving partial differential equations on a closed surface, based on a technique for discretizing the surface introduced by Wenjun Ying and Wei-Cheng Wang ( J. Comput.
Edit intent: clarity
Original: We present a general purpose method for solving partial differential equations on a closed surface, using a technique for discretizing the surface introduced by Wenjun Ying and Wei-Cheng Wang ( J. Comput.
Revised: We present a general purpose method for solving partial differential equations on a closed surface, using a technique for discretizing the surface introduced by Wenjun Ying and Wei-Cheng Wang J. Comput.
Edit intent: fluency
Original:  We obtain second order accuracy for solutions of a variety of equations, including surface diffusion determined by the Laplace-Beltrami operator and the shallow water equations on a sphere.
Revised:  We observe second order accuracy for solutions of a variety of equations, including surface diffusion determined by the Laplace-Beltrami operator and the shallow water equations on a sphere.
Edit intent: clarity