wanyu/IteraTeR_v2 huggingface dataset:
Original:  We prove that the number of parameters used to describe the employed DNN grows at most polynomially in both the  reciprocal of the prescribed approximation accuracy \varepsilon > 0 and the PDE dimension d \in N . A crucial ingredient in our proof is the fact that the artificial neural network used to approximate the solution of the PDE is indeed a deep artificial neural network with a large number of hidden layers.
Revised:  We prove that the number of parameters used to describe the employed DNN grows at most polynomially in both the reciprocal of the prescribed approximation accuracy \varepsilon > 0 . A crucial ingredient in our proof is the fact that the artificial neural network used to approximate the solution of the PDE is indeed a deep artificial neural network with a large number of hidden layers.
Edit intent: clarity
Original:  Here , we investigate international trade through the lenses of the single-layer, multiplex, and multi-layer networks.
Revised:  Here we investigate international trade through the lenses of the single-layer, multiplex, and multi-layer networks.
Edit intent: fluency
Original: We study polynomial time algorithms for estimating the mean of a random vector X in R^d from n independent samples X_1,\ldots,X_n when X may be heavy-tailed  .
Revised: We study polynomial time algorithms for estimating the mean of a heavy-tailed .
Edit intent: clarity
Original:  In particular, for confidence \delta > 0, the empirical mean has confidence intervals with radius of order \text{Tr \Sigma / \delta n rather than \text{Tr \Sigma /n } + \sqrt{ \max(\Sigma) \log (1/\delta) / n} from the Gaussian case.
Revised:  rather than \text{Tr \Sigma /n } + \sqrt{ \max(\Sigma) \log (1/\delta) / n} from the Gaussian case.
Edit intent: coherence
Original:  } We offer the first polynomial time algorithm to estimate the mean with sub-Gaussian confidence intervals under such mild assumptions.
Revised:  } We offer the first polynomial time algorithm to estimate the mean with sub-Gaussian-size confidence intervals under such mild assumptions.
Edit intent: clarity
Original: We propose SoaAlloc, a dynamic object allocator for Single-Method Multiple-Objects applications in CUDA. SoaAlloc is the first allocator for GPUs that (a ) arranges allocations in a SIMD-friendly Structure of Arrays (SOA)data layout, (b) provides a do-all operation for maximizing the benefit of SOA, and (c) is on par with state-of-the-art memory allocators for raw (de)allocation time.
Revised: Object-oriented programming (OOP) has long been regarded as too inefficient for SIMD high-performance computing, despite the fact that many important HPC applications have an inherent object structure. We discovered a broad subset of OOP that can be implemented efficiently on massively parallel SIMD accelerators. We call it Single-Method Multiple-Objects applications in CUDA. SoaAlloc is the first allocator for GPUs that (a ) arranges allocations in a SIMD-friendly Structure of Arrays (SOA)data layout, (b) provides a do-all operation for maximizing the benefit of SOA, and (c) is on par with state-of-the-art memory allocators for raw (de)allocation time.
Edit intent: coherence
Original: We prove the superhedging duality for a discrete-time financial market with proportional transaction costs under portfolio constraints and model uncertainty.
Revised: We prove the superhedging duality for a discrete-time financial market with proportional transaction costs under model uncertainty.
Edit intent: clarity
Original:  To obtain this result we first need to revisit the classical extended Krylov subspace algorithm and prove that the projected matrix can be written efficiently as a structured matrix-pair , where the structure can take several forms, such as , e.g., Hessenberg or inverse Hessenberg.
Revised:  To obtain this framework we revisit the classical extended Krylov subspace algorithm and prove that the projected matrix can be written efficiently as a structured matrix-pair , where the structure can take several forms, such as , e.g., Hessenberg or inverse Hessenberg.
Edit intent: clarity
Original:  To obtain this result we first need to revisit the classical extended Krylov subspace algorithm and prove that the projected matrix can be written efficiently as a structured matrix-pair , where the structure can take several forms, such as , e.g., Hessenberg or inverse Hessenberg.
Revised:  To obtain this result we first need to revisit the classical extended Krylov subspace algorithm and prove that the projected matrix can be written efficiently as a structured pencil , where the structure can take several forms, such as , e.g., Hessenberg or inverse Hessenberg.
Edit intent: clarity
Original:  To obtain this result we first need to revisit the classical extended Krylov subspace algorithm and prove that the projected matrix can be written efficiently as a structured matrix-pair , where the structure can take several forms, such as , e.g., Hessenberg or inverse Hessenberg.
Revised:  To obtain this result we first need to revisit the classical extended Krylov subspace algorithm and prove that the projected matrix can be written efficiently as a structured matrix-pair , where the structure can take several forms, such as Hessenberg or inverse Hessenberg.
Edit intent: coherence
Original:   Based on the compact storage of a tridiagonal matrix-pair in the biorthogonal setting, we can develop short recurrences.
Revised:  Based on the compact storage of this tridiagonal pencil in the biorthogonal setting, we can develop short recurrences.
Edit intent: clarity
Original:  The numerical experiments confirm the validity of the approach.
Revised:  Numerical experiments confirm the validity of the approach.
Edit intent: clarity
Original: In this paper, we present a robust sinusoidal model fitting method based on the Differential Evolution (DE) algorithm for determining cardiopulmonary resuscitation (CPR) quality-parameters - naming chest compression frequency and depth - as measured by an inertial sensor placed at the wrist  .
Revised: In this paper, a robust sinusoidal model fitting method based on the Differential Evolution (DE) algorithm for determining cardiopulmonary resuscitation (CPR) quality-parameters - naming chest compression frequency and depth - as measured by an inertial sensor placed at the wrist .
Edit intent: clarity
Original:  Once included into a smartphone or smartwatch app, our proposed algorithm will enable laypersons to improve cardiopulmonary resuscitation (as part of a continuous closed-loop support-system).
Revised:  Once included into a smartphone or smartwatch app, the proposed algorithm will enable laypersons to improve cardiopulmonary resuscitation (as part of a continuous closed-loop support-system).
Edit intent: fluency
Original:  Once included into a smartphone or smartwatch app, our proposed algorithm will enable laypersons to improve cardiopulmonary resuscitation (as part of a continuous closed-loop support-system).
Revised:  Once included into a smartphone or smartwatch app, our proposed algorithm will enable bystanders to improve CPR (as part of a continuous closed-loop support-system).
Edit intent: clarity
Original:  By evaluating the sensitivity of the model with data recorded by a Laerdal Resusci Anne mannequin as reference standard, a low variance for compression frequency of +-2.7 cpm (2.5 \%) \pm  has been found for the sensor placed at the wrist, making this previously not evaluated position a suitable alternative to the typical smartphone placement in the hand  .
Revised:  By evaluating the precision of the model with data recorded by a Laerdal Resusci Anne mannequin as reference standard, a low variance for compression frequency of +-2.7 cpm (2.5 \%) \pm has been found for the sensor placed at the wrist, making this previously not evaluated position a suitable alternative to the typical smartphone placement in the hand .
Edit intent: clarity
Original:  By evaluating the sensitivity of the model with data recorded by a Laerdal Resusci Anne mannequin as reference standard, a low variance for compression frequency of +-2.7 cpm (2.5 \%) \pm  has been found for the sensor placed at the wrist, making this previously not evaluated position a suitable alternative to the typical smartphone placement in the hand  .
Revised:  By evaluating the sensitivity of the model with data recorded by a Laerdal Resusci Anne mannequin as reference standard, a low variance for compression frequency of \pm has been found for the sensor placed at the wrist, making this previously not evaluated position a suitable alternative to the typical smartphone placement in the hand .
Edit intent: coherence
Original:  By evaluating the sensitivity of the model with data recorded by a Laerdal Resusci Anne mannequin as reference standard, a low variance for compression frequency of +-2.7 cpm (2.5 \%) \pm  has been found for the sensor placed at the wrist, making this previously not evaluated position a suitable alternative to the typical smartphone placement in the hand  .
Revised:  By evaluating the sensitivity of the model with data recorded by a Laerdal Resusci Anne mannequin as reference standard, a low variance for compression frequency of +-2.7 cpm (2.5 \%) \pm has been found for the sensor placed at the wrist, making this previously unconsidered position a suitable alternative to the typical smartphone placement in the hand .
Edit intent: clarity
Original:  By evaluating the sensitivity of the model with data recorded by a Laerdal Resusci Anne mannequin as reference standard, a low variance for compression frequency of +-2.7 cpm (2.5 \%) \pm  has been found for the sensor placed at the wrist, making this previously not evaluated position a suitable alternative to the typical smartphone placement in the hand  .
Revised:  By evaluating the sensitivity of the model with data recorded by a Laerdal Resusci Anne mannequin as reference standard, a low variance for compression frequency of +-2.7 cpm (2.5 \%) \pm has been found for the sensor placed at the wrist, making this previously not evaluated position a suitable alternative to the typical placement in the hand .
Edit intent: clarity
Original:  Synthetic antibodies capable of bivalently binding within single Env trimers (intra-spike crosslinking) were previously shown to exhibit increased neutralization potencies.
Revised:  Synthetic antibodies designed to bivalently bind a single Env trimer (intra-spike crosslinking) were previously shown to exhibit increased neutralization potencies.
Edit intent: clarity
Original:  Model predictions , verified by experimental data, show that although a long flexible polymer may be capable of bivalent binding, it exhibits weak neutralization due to the large loss in entropic degrees of freedom during bivalent binding .
Revised:  Model predictions suggest that while a long flexible polymer may be capable of bivalent binding, it exhibits weak neutralization due to the large loss in entropic degrees of freedom during bivalent binding .
Edit intent: clarity
Original:  In contrast, the strongest neutralization potencies  require a rigid linker that optimally spans the distance between two Fab binding sites on an Env trimer  .
Revised:  In contrast, the strongest neutralization potencies are predicted to require a rigid linker that optimally spans the distance between two Fab binding sites on an Env trimer .
Edit intent: clarity
Original: This paper proposes a method for efficient training of the Q-function for continuous-state Markov Decision Processes (MDP), such that the traces of the resulting policies satisfy a Linear Temporal Logic (LTL) property.
Revised: This paper proposes a method for efficient training of Q-function for continuous-state Markov Decision Processes (MDP), such that the traces of the resulting policies satisfy a Linear Temporal Logic (LTL) property.
Edit intent: clarity
Original:  The control policy is then synthesized by a reinforcement learning algorithm assuming that no prior knowledge is available from the MDP.
Revised:  The control policy is then synthesised by a reinforcement learning algorithm assuming that no prior knowledge is available from the MDP.
Edit intent: fluency
Original: This paper proposes a method for efficient training of Q-function for continuous-state Markov Decision Processes ( MDP) , such that the traces of the resulting policies satisfy a  Linear Temporal Logic (LTL) property.
Revised: We propose a method for efficient training of Q-function for continuous-state Markov Decision Processes ( MDP) , such that the traces of the resulting policies satisfy a Linear Temporal Logic (LTL) property.
Edit intent: clarity
Original: This paper proposes a method for efficient training of Q-function for continuous-state Markov Decision Processes ( MDP) , such that the traces of the resulting policies satisfy a  Linear Temporal Logic (LTL) property.
Revised: This paper proposes a method for efficient training of Q-functions for continuous-state Markov Decision Processes ( MDP) , such that the traces of the resulting policies satisfy a Linear Temporal Logic (LTL) property.
Edit intent: fluency
Original: This paper proposes a method for efficient training of Q-function for continuous-state Markov Decision Processes ( MDP) , such that the traces of the resulting policies satisfy a  Linear Temporal Logic (LTL) property.
Revised: This paper proposes a method for efficient training of Q-function for continuous-state Markov Decision Processes ( MDPs) such that the traces of the resulting policies satisfy a Linear Temporal Logic (LTL) property.
Edit intent: fluency
Original: This paper proposes a method for efficient training of Q-function for continuous-state Markov Decision Processes ( MDP) , such that the traces of the resulting policies satisfy a  Linear Temporal Logic (LTL) property.
Revised: This paper proposes a method for efficient training of Q-function for continuous-state Markov Decision Processes ( MDP) , such that the traces of the resulting policies satisfy a given Linear Temporal Logic (LTL) property.
Edit intent: clarity
Original:  We convert the LTL property into a limit deterministic Buchi automaton with which a synchronized product MDPis constructed .
Revised:  We convert the LTL property into a limit deterministic Buchi automaton and construct an on-the-fly synchronised product MDP .
Edit intent: clarity
Original:  The proposed method is evaluated in a numerical study to test the quality of the generated control policy and is compared against conventional methods for policy synthesis such as MDP abstraction (Voronoi quantizer) and approximate dynamic programming (fitted value iteration).
Revised:  The proposed method is evaluated in a numerical study to test the quality of the generated control policy and is compared with conventional methods for policy synthesis such as MDP abstraction (Voronoi quantizer) and approximate dynamic programming (fitted value iteration).
Edit intent: fluency
Original:  In this work, we explore the use of hardware/software co-design and hardware acceleration to significantly reduce the exe-cution time of short sequence alignment, a crucial step in analyzing sequenced genomes.
Revised:  In this work, we explore the use of hardware/software co-design and hardware acceleration to significantly reduce the execution time of short sequence alignment, a crucial step in analyzing sequenced genomes.
Edit intent: fluency
Original:  The first key idea of our pro-posed pre-alignment filter is to provide high filtering accuracy by correctly detecting all common subsequences shared between two given sequences.
Revised:  The first key idea of our proposed pre-alignment filter is to provide high filtering accuracy by correctly detecting all common subsequences shared between two given sequences.
Edit intent: fluency
Original:  The second key idea is to design a hardware accelerator design that adopts modern FPGA (field-programmable gate array) architectures to fur-ther boost the performance of our algorithm.
Revised:  The second key idea is to design a hardware accelerator design that adopts modern FPGA (field-programmable gate array) architectures to further boost the performance of our algorithm.
Edit intent: fluency
Original:  The addition of SLIDER as a pre-alignment step reduces the execution time of five state-of-the-art sequence align-ers by up to 18.8x. SLIDER can be adopted for any bioinformatics pipeline that performs sequence alignment for verification.
Revised:  The addition of SLIDER as a pre-alignment step reduces the execution time of five state-of-the-art sequence aligners by up to 18.8x. SLIDER can be adopted for any bioinformatics pipeline that performs sequence alignment for verification.
Edit intent: fluency
Original: Motivation: The ability to generate massive amounts of sequencing data continues to overwhelm the processing capacity of existing algorithms and compute infrastructures.
Revised: Motivation: The ability to generate massive amounts of sequencing data continues to overwhelm the processing capability of existing algorithms and compute infrastructures.
Edit intent: clarity
Original:  We introduce Shouji, a highly parallel and accurate pre-alignment filter that remarkably reduces the need for computationally-costly dynamic programming algorithms.
Revised:  We introduce Shouji, a highly-parallel and accurate pre-alignment filter that remarkably reduces the need for computationally-costly dynamic programming algorithms.
Edit intent: fluency
Original:  The second key idea is to design a hardware accelerator design that adopts modern FPGA ( field-programmable gate array ) architectures to further boost the performance of our algorithm.
Revised:  The second key idea is to design a hardware accelerator that adopts modern FPGA ( field-programmable gate array ) architectures to further boost the performance of our algorithm.
Edit intent: clarity
Original:  The second key idea is to design a hardware accelerator design that adopts modern FPGA ( field-programmable gate array ) architectures to further boost the performance of our algorithm.
Revised:  The second key idea is to design a hardware accelerator design that adopts modern FPGA ( Field-Programmable Gate Array ) architectures to further boost the performance of our algorithm.
Edit intent: fluency
Original:  Our FPGA accelerator is up to three orders of magnitude faster than the equivalent CPU implementation of Shouji.
Revised:  Our FPGA-based accelerator is up to three orders of magnitude faster than the equivalent CPU implementation of Shouji.
Edit intent: clarity
Original:  The addition of Shouji as a pre-alignment step reduces the execution time of  five state-of-the-art sequence aligners by up to 18.8x. Shouji can be adopted for any bioinformatics pipeline that performs sequence alignment for verification.
Revised:  The addition of Shouji as a pre-alignment step reduces the execution time of the five state-of-the-art sequence aligners by up to 18.8x. Shouji can be adopted for any bioinformatics pipeline that performs sequence alignment for verification.
Edit intent: fluency
Original:  The addition of Shouji as a pre-alignment step reduces the execution time of  five state-of-the-art sequence aligners by up to 18.8x. Shouji can be adopted for any bioinformatics pipeline that performs sequence alignment for verification.
Revised:  The addition of Shouji as a pre-alignment step reduces the execution time of five state-of-the-art sequence aligners by up to 18.8x. Shouji can be adapted for any bioinformatics pipeline that performs sequence alignment for verification.
Edit intent: fluency
Original:  The ground-breaking algorithm of Moser and Tardos  made the LLL fully constructive, following earlier works by Beckand Alon0pt and Alon~\mbox{ alon_lll }0pt } giving algorithms under significantly stronger LLL-like conditions.
Revised:  The ground-breaking algorithm of Moser and Tardos made the LLL fully constructive, following earlier results by Beck~\mbox{ beck_lll0pt and Alon~\mbox{ alon_lll }0pt } giving algorithms under significantly stronger LLL-like conditions.
Edit intent: clarity
Original:  In fact, our techniques yields LCAs for settings beyond the standard LLL condition.
Revised:  In fact, our techniques yield LCAs for settings beyond the standard LLL condition.
Edit intent: fluency
Original:  As decisions are based on how the data is fused, we propose two measuring models- one optimistic and another conservative.
Revised:  As decisions are based on how the data is fused, we propose two measuring models: one optimistic and another conservative.
Edit intent: fluency
Original: Applications in political redistricting demand quantitative measures of geometric compactness to distinguish between simple and contorted shapes of legislative voting districts .
Revised: Applications such as political redistricting demand quantitative measures of geometric compactness to distinguish between simple and contorted shapes of legislative voting districts .
Edit intent: clarity
Original: Applications in political redistricting demand quantitative measures of geometric compactness to distinguish between simple and contorted shapes of legislative voting districts .
Revised: Applications in political redistricting demand quantitative measures of geometric compactness to distinguish between simple and contorted shapes .
Edit intent: clarity
Original:  These issues are addressed in theory by the isoperimetric profile, which plots the minimum perimeter needed to inscribe shapes of different prescribed areas within the boundary of a shape ;
Revised:  These issues are addressed in theory by the isoperimetric profile, which plots the minimum perimeter needed to inscribe regions of different prescribed areas within the boundary of a shape ;
Edit intent: clarity
Original:  These issues are addressed in theory by the isoperimetric profile, which plots the minimum perimeter needed to inscribe shapes of different prescribed areas within the boundary of a shape ;
Revised:  These issues are addressed in theory by the isoperimetric profile, which plots the minimum perimeter needed to inscribe shapes of different prescribed areas within the boundary of a shape . Efficient
Edit intent: coherence
Original: Most existing recommender systems leverage the data of one type of user behaviors only , such as the purchase behavior  in E-commerce that is directly related to the business KPI (Key Performance Indicator) of conversion rate.
Revised: Most existing recommender systems leverage user behavior data of one type of user behaviors only , such as the purchase behavior in E-commerce that is directly related to the business KPI (Key Performance Indicator) of conversion rate.
Edit intent: fluency
Original: Most existing recommender systems leverage the data of one type of user behaviors only , such as the purchase behavior  in E-commerce that is directly related to the business KPI (Key Performance Indicator) of conversion rate.
Revised: Most existing recommender systems leverage the data of one type , such as the purchase behavior in E-commerce that is directly related to the business KPI (Key Performance Indicator) of conversion rate.
Edit intent: clarity
Original:  Besides the key behavioral data, we argue that other forms of user behaviors also provide valuable signal on a user's preference , such as views, clicks, adding a product to shop carts and so on.
Revised:  Besides the key behavioral data, we argue that other types of user behavior data also provide valuable signal on a user's preference , such as views, clicks, adding a product to shop carts and so on.
Edit intent: clarity
Original:  Besides the key behavioral data, we argue that other forms of user behaviors also provide valuable signal on a user's preference , such as views, clicks, adding a product to shop carts and so on.
Revised:  Besides the key behavioral data, we argue that other forms of user behaviors also provide valuable signal , such as views, clicks, adding a product to shop carts and so on.
Edit intent: clarity