wanyu/IteraTeR_v2 huggingface dataset:
Original: In this paper, we focus on one of the key technologies for the fifth-generation wireless communication networks, massive multiple-input-multiple-output (mMIMO), by investigating two of its most relevant architectures: 1) to provide in-band wireless backhauling to a dense deployment of self-backhauled small cells (SCs) acting as communication relays to end-users , and 2) to provide direct wireless access (DA) to end-users .
Revised: In this paper, we focus on one of the key technologies for the fifth-generation wireless communication networks, massive multiple-input-multiple-output (mMIMO), by investigating two of its most relevant architectures: 1) to provide in-band backhaul for the ultra-dense network (UDN) of self-backhauled small cells (SCs) acting as communication relays to end-users , and 2) to provide direct wireless access (DA) to end-users .
Edit intent: clarity
Original: In this paper, we focus on one of the key technologies for the fifth-generation wireless communication networks, massive multiple-input-multiple-output (mMIMO), by investigating two of its most relevant architectures: 1) to provide in-band wireless backhauling to a dense deployment of self-backhauled small cells (SCs) acting as communication relays to end-users , and 2) to provide direct wireless access (DA) to end-users .
Revised: In this paper, we focus on one of the key technologies for the fifth-generation wireless communication networks, massive multiple-input-multiple-output (mMIMO), by investigating two of its most relevant architectures: 1) to provide in-band wireless backhauling to a dense deployment of self-backhauled small cells (SCs) , and 2) to provide direct wireless access (DA) to end-users .
Edit intent: clarity
Original: In this paper, we focus on one of the key technologies for the fifth-generation wireless communication networks, massive multiple-input-multiple-output (mMIMO), by investigating two of its most relevant architectures: 1) to provide in-band wireless backhauling to a dense deployment of self-backhauled small cells (SCs) acting as communication relays to end-users , and 2) to provide direct wireless access (DA) to end-users .
Revised: In this paper, we focus on one of the key technologies for the fifth-generation wireless communication networks, massive multiple-input-multiple-output (mMIMO), by investigating two of its most relevant architectures: 1) to provide in-band wireless backhauling to a dense deployment of self-backhauled small cells (SCs) acting as communication relays to end-users , and 2) to provide direct access (DA) to end-users .
Edit intent: clarity
Original:  Through comprehensive 3GPP-based system-level simulations and analytical formulation , we show the end-to-end user rates achievable with these two architectures.
Revised:  Through comprehensive 3GPP-based system-level simulations and analytical formulations , we show the end-to-end user rates achievable with these two architectures.
Edit intent: fluency
Original:  Through comprehensive 3GPP-based system-level simulations and analytical formulation , we show the end-to-end user rates achievable with these two architectures.
Revised:  Through comprehensive 3GPP-based system-level simulations and analytical formulation , we show the end-to-end UE rates achievable with these two architectures.
Edit intent: style
Original:  Different from the existing work , we provide results for two strategies of self-backhauled SCs deployments, namely random and ad-hoc .
Revised:  Differently from the existing work , we provide results for two strategies of self-backhauled SCs deployments, namely random and ad-hoc .
Edit intent: fluency
Original:  Different from the existing work , we provide results for two strategies of self-backhauled SCs deployments, namely random and ad-hoc .
Revised:  Different from the existing works , we provide results for two strategies of self-backhauled SCs deployments, namely random and ad-hoc .
Edit intent: fluency
Original:  Different from the existing work , we provide results for two strategies of self-backhauled SCs deployments, namely random and ad-hoc .
Revised:  Different from the existing work , we provide results for two strategies of self-backhauled SC deployments, namely random and ad-hoc .
Edit intent: fluency
Original:  We also show the optimal backhaul and access time resource partition due to the in-band self-backhauling operations.
Revised:  We also evaluate the optimal backhaul and access time resource partition due to the in-band self-backhauling operations.
Edit intent: clarity
Original:  We find that the ad-hoc deployment of self-backhauled SCs closer to the users (UEs ) with optimal resource partition and with directive antenna patterns, provides rate improvements for cell-edge UEs that amount to 30\% , and a tenfold gain as compared to mMIMO DA architecture with pilot reuse 3 and reuse 1, respectively.
Revised:  We find that the ad-hoc deployment of self-backhauled SCs closer to the UEs with optimal resource partition and with directive antenna patterns, provides rate improvements for cell-edge UEs that amount to 30\% , and a tenfold gain as compared to mMIMO DA architecture with pilot reuse 3 and reuse 1, respectively.
Edit intent: clarity
Original:  We find that the ad-hoc deployment of self-backhauled SCs closer to the users (UEs ) with optimal resource partition and with directive antenna patterns, provides rate improvements for cell-edge UEs that amount to 30\% , and a tenfold gain as compared to mMIMO DA architecture with pilot reuse 3 and reuse 1, respectively.
Revised:  We find that the ad-hoc deployment of self-backhauled SCs closer to the users (UEs ) with optimal resource partition and with directive antenna patterns, provides rate improvements for cell-edge UEs that amount to 30\% and tenfold gain, as compared to mMIMO DA architecture with pilot reuse 3 and reuse 1, respectively.
Edit intent: fluency
Original:  On the other hand, mMIMO s-BH underperforms mMIMO DA above the median  of the UE rates when the UEs are in the center of the cell, and the effect of pilot contamination is mitigated .
Revised:  On the other hand, mMIMO s-BH underperforms mMIMO DA above the median value of the UE rates when the UEs are in the center of the cell, and the effect of pilot contamination is mitigated .
Edit intent: clarity
Original:  On the other hand, mMIMO s-BH underperforms mMIMO DA above the median  of the UE rates when the UEs are in the center of the cell, and the effect of pilot contamination is mitigated .
Revised:  On the other hand, mMIMO s-BH underperforms mMIMO DA above the median of the UE rates when the effect of pilot contamination is mitigated .
Edit intent: clarity
Original:  In this work, we first illustrate this point by considering the classic example of the single-enzyme, single-substrate Michaelis-Menten reaction mechanism.
Revised:  In this work, we first illustrate this point by considering the classic example of the single-enzyme, single-substrate Michaelis--Menten reaction mechanism.
Edit intent: fluency
Original:  In this case, depending on the ordering of the relevant timescales, either two or three dynamic regimes can emerge.
Revised:  In this case, depending on the ordering of the relevant timescales, several dynamic regimes can emerge.
Edit intent: clarity
Original:  In addition to the characteristic timescales for these regimes, we derive matching timescales that precisely determine when the transitions from initial fast transient to steady-state kinetics occurs.
Revised:  In addition to the characteristic timescales for these regimes, we derive matching timescales that determine (approximately) when the transitions from initial fast transient to steady-state kinetics occurs.
Edit intent: clarity
Original:  To achieve a considerable speedup , a hyper-reduction step is needed to reduce the computational complexity due to nonlinear terms.
Revised:  To achieve a considerable speed-up , a hyper-reduction step is needed to reduce the computational complexity due to nonlinear terms.
Edit intent: fluency
Original:  In contrast to the traditional hyper-reduction techniques where the collection of nonlinear term snapshots is required, the SNS method completely avoids the use of the nonlinear term snapshots.
Revised:  In contrast to the traditional hyper-reduction techniques where the collection of nonlinear term snapshots is required, the SNS method avoids collecting the nonlinear term snapshots.
Edit intent: coherence
Original: Several reduced order models have been successfully developed for nonlinear dynamical systems.
Revised: Several reduced order models have been developed for nonlinear dynamical systems.
Edit intent: clarity
Original:  because ST-GNAT involves an expensive offline cost related to collecting nonlinear term snapshots . Error analysis shows that the oblique projection error bound of the SNS method depends on the condition number of the volume matrix generated from a discretization of a specific numerical scheme . Numerical results support that the accuracy of the solution from the SNS method is comparable to the traditional methods and a considerable speed-up (i.e., a factor of two to a hundred)
Revised:  because ST-GNAT involves an expensive offline cost related to collecting nonlinear term snapshots . Numerical results support that the accuracy of the solution from the SNS method is comparable to the traditional methods and a considerable speed-up (i.e., a factor of two to a hundred)
Edit intent: coherence
Original: We introduce a quantum algorithm for solving structured-prediction problems with a runtime that scales with the square root of the size of the label space, but scales in \widetilde O\left( \frac{1{\epsilon^5}}  \right) with respect to the precision of the solution.
Revised: We introduce a quantum algorithm for solving structured prediction problems with a runtime that scales with the square root of the size of the label space, but scales in \widetilde O\left( \frac{1{\epsilon^5}} \right) with respect to the precision of the solution.
Edit intent: fluency
Original: We introduce a quantum algorithm for solving structured prediction problems  with a runtime that scales with the square root of the size of the label space, but scales in \widetilde O\left( \epsilon^{-3.5 \right) with respect to the precision, \epsilon, of the solution.
Revised: We introduce a quantum algorithm for solving structured prediction problems with a runtime that scales with the square root of the size of the label space, and in \widetilde O\left( \epsilon^{-3.5 \right) with respect to the precision, \epsilon, of the solution.
Edit intent: coherence
Original:  Our algorithm uses quantum Gibbs sampling at temperature \Omega (\epsilon) as a subroutine.
Revised:  This algorithm uses quantum Gibbs sampling at temperature \Omega (\epsilon) as a subroutine.
Edit intent: fluency
Original:  Numerical results using Monte Carlo simulations on an image tagging task demonstrate the benefit of the approach.
Revised:  Our numerical results using Monte Carlo simulations on an image tagging task demonstrate the benefit of the approach.
Edit intent: fluency
Original:  We  show that a stochastic subgradient descent method that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the structured prediction problem with a runtime that scales with the square root of the size of the label space, and in \widetilde O\left(1/\epsilon\right) with respect to the precision, \epsilon, of the solution.
Revised:  We first show that a stochastic subgradient descent method that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the structured prediction problem with a runtime that scales with the square root of the size of the label space, and in \widetilde O\left(1/\epsilon\right) with respect to the precision, \epsilon, of the solution.
Edit intent: coherence
Original:  We  show that a stochastic subgradient descent method that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the structured prediction problem with a runtime that scales with the square root of the size of the label space, and in \widetilde O\left(1/\epsilon\right) with respect to the precision, \epsilon, of the solution.
Revised:  We show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the structured prediction problem with a runtime that scales with the square root of the size of the label space, and in \widetilde O\left(1/\epsilon\right) with respect to the precision, \epsilon, of the solution.
Edit intent: clarity
Original:  Motivated by robust inference techniques in machine learning, we  introduce another quantum algorithm that solves a smooth approximation of the structured prediction problem with a similar quantum speedup in the size of the label space and a similar scaling in the precision parameter.
Revised:  Motivated by robust inference techniques in machine learning, we then introduce another quantum algorithm that solves a smooth approximation of the structured prediction problem with a similar quantum speedup in the size of the label space and a similar scaling in the precision parameter.
Edit intent: coherence
Original:  In doing so, we analyze a stochastic gradient algorithm for convex optimization in the presence of an additive error in the calculation of the gradients, and show that its convergence rate does not deteriorate if the additive errors are of the order O(\sqrt\epsilon).
Revised:  In doing so, we analyze a variant of stochastic gradient descent for convex optimization in the presence of an additive error in the calculation of the gradients, and show that its convergence rate does not deteriorate if the additive errors are of the order O(\sqrt\epsilon).
Edit intent: clarity
Original: The\delta-Coin Problem is the of uniform AC^0[\oplus] formulas of depth d and size n^k form an infinite hierarchy.
Revised: \delta-Coin Problem is the of uniform AC^0[\oplus] formulas of depth d and size n^k form an infinite hierarchy.
Edit intent: fluency
Original: The\delta-Coin Problem is the of uniform AC^0[\oplus] formulas of depth d and size n^k form an infinite hierarchy.
Revised: The is the of uniform AC^0[\oplus] formulas of depth d and size n^k form an infinite hierarchy.
Edit intent: coherence
Original:  For this, we find the first class of explicit functions giving (up to polynomial factor) matching upper and lower bounds for AC^0[\oplus] formulas, derived from the \delta-Coin Problem, the } computational problem of distinguishing between coins that are heads with probability (1+\delta)/2 or (1-\delta)/2, where \delta is a parameter tending to 0.
Revised:  For this, we find the first class of explicit functions giving (up to polynomial factor) matching upper and lower bounds for AC^0[\oplus] formulas, derived from the \delta-Coin Problem, the } computational problem of distinguishing between coins that are heads with probability (1+\delta)/2 or (1-\delta)/2, where \delta is a parameter going to 0.
Edit intent: clarity
Original:  We study this problem's complexity in the model of constant-depth Boolean circuits and prove the following results.
Revised:  We study this problem's complexity 
Edit intent: clarity
Original:  For any constant d\geq 2, we show that there areexplicit monotone AC^0 formulas (i.e. made up of AND and OR gates only) solving the \delta-coin problem, having depth d, size \exp(O(d(1/\delta)^{1/(d-1)})), and sample complexity (no. of inputs) poly(1/\delta) \ge2 .
Revised:  explicit monotone AC^0 formulas (i.e. made up of AND and OR gates only) solving the \delta-coin problem, having depth d, size \exp(O(d(1/\delta)^{1/(d-1)})), and sample complexity (no. of inputs) poly(1/\delta) \ge2 .
Edit intent: clarity
Original:  For any constant d\geq 2, we show that there areexplicit monotone AC^0 formulas (i.e. made up of AND and OR gates only) solving the \delta-coin problem, having depth d, size \exp(O(d(1/\delta)^{1/(d-1)})), and sample complexity (no. of inputs) poly(1/\delta) \ge2 .
Revised:  For any constant d\geq 2, we show that there areexplicit monotone AC^0 formulas solving the \delta-coin problem, having depth d, size \exp(O(d(1/\delta)^{1/(d-1)})), and sample complexity (no. of inputs) poly(1/\delta) \ge2 .
Edit intent: clarity
Original:  For any constant d\geq 2, we show that there areexplicit monotone AC^0 formulas (i.e. made up of AND and OR gates only) solving the \delta-coin problem, having depth d, size \exp(O(d(1/\delta)^{1/(d-1)})), and sample complexity (no. of inputs) poly(1/\delta) \ge2 .
Revised:  For any constant d\geq 2, we show that there areexplicit monotone AC^0 formulas (i.e. made up of AND and OR gates only) solving the \delta-coin problem, having depth d, size \exp(O(d(1/\delta)^{1/(d-1)})), and sample complexity poly(1/\delta) \ge2 .
Edit intent: clarity
Original:  For any constant d\geq 2, we show that there areexplicit monotone AC^0 formulas (i.e. made up of AND and OR gates only) solving the \delta-coin problem, having depth d, size \exp(O(d(1/\delta)^{1/(d-1)})), and sample complexity (no. of inputs) poly(1/\delta) \ge2 .
Revised:  For any constant d\geq 2, we show that there areexplicit monotone AC^0 formulas (i.e. made up of AND and OR gates only) solving the \delta-coin problem, having depth d, size \exp(O(d(1/\delta)^{1/(d-1)})), and sample complexity (no. of inputs) poly(1/\delta) , for constant d\ge2 .
Edit intent: clarity
Original:  This matches previous upper bounds of O'Donnell and Wimmer (ICALP 2007) and Amano (ICALP 2009) in terms of size (which is optimal) and improves the sample complexity from \exp(O(d(1/\delta)^{1/(d-1))) to poly(1/\delta).
Revised:  This matches previous upper bounds of O'Donnell and Wimmer (ICALP 2007) and Amano (ICALP 2009) in terms of size and improves the sample complexity from \exp(O(d(1/\delta)^{1/(d-1))) to poly(1/\delta).
Edit intent: clarity
Original:  We show that the above upper bounds are nearly tight even for the significantly stronger model of AC^0[\oplus] formulas ( i.e. allowing NOT and Parity gates): formally, we show that any AC^0[\oplus] formula solving the \delta-coin problem must have size \exp(\Omega(d(1/\delta)^{1/(d-1)})).
Revised:  We show that the above upper bounds are nearly tight even for the stronger model of AC^0[\oplus] formulas ( i.e. allowing NOT and Parity gates): formally, we show that any AC^0[\oplus] formula solving the \delta-coin problem must have size \exp(\Omega(d(1/\delta)^{1/(d-1)})).
Edit intent: clarity
Original:  We show that the above upper bounds are nearly tight even for the significantly stronger model of AC^0[\oplus] formulas ( i.e. allowing NOT and Parity gates): formally, we show that any AC^0[\oplus] formula solving the \delta-coin problem must have size \exp(\Omega(d(1/\delta)^{1/(d-1)})).
Revised:  We show that the above upper bounds are nearly tight even for the significantly stronger model of AC^0[\oplus] formulas ( which allow NOT and Parity gates): formally, we show that any AC^0[\oplus] formula solving the \delta-coin problem must have size \exp(\Omega(d(1/\delta)^{1/(d-1)})).
Edit intent: clarity
Original:  We show that the above upper bounds are nearly tight even for the significantly stronger model of AC^0[\oplus] formulas ( i.e. allowing NOT and Parity gates): formally, we show that any AC^0[\oplus] formula solving the \delta-coin problem must have size \exp(\Omega(d(1/\delta)^{1/(d-1)})).
Revised:  We show that the above upper bounds are nearly tight even for the significantly stronger model of AC^0[\oplus] formulas ( i.e. allowing NOT and Parity gates): any AC^0[\oplus] formula solving the \delta-coin problem must have size \exp(\Omega(d(1/\delta)^{1/(d-1)})).
Edit intent: coherence
Original:  This strengthens a result of Cohen, Ganor and Raz (APPROX-RANDOM 2014), who prove a similar result for AC^0, and a result of Shaltiel and Viola (SICOMP 2010), which implies a superpolynomially weaker (still exponential) lower bound.
Revised:  This strengthens a result of Cohen, Ganor and Raz (APPROX-RANDOM 2014), who prove a similar result for AC^0, and a result of Shaltiel and Viola (SICOMP 2010), who give a superpolynomially weaker (still exponential) lower bound.
Edit intent: clarity
Original:  The above yields the first class of\textit{explicit functions where we have nearly (up to a polynomial factor) matching upper and lower bounds for the class of AC^0[\oplus] formulas.
Revised:  The \textit{explicit functions where we have nearly (up to a polynomial factor) matching upper and lower bounds for the class of AC^0[\oplus] formulas.
Edit intent: clarity
Original:  The above yields the first class of\textit{explicit functions where we have nearly (up to a polynomial factor) matching upper and lower bounds for the class of AC^0[\oplus] formulas.
Revised:  The above yields the first class of\textit{ functions where we have nearly (up to a polynomial factor) matching upper and lower bounds for the class of AC^0[\oplus] formulas.
Edit intent: clarity
Original:  In particular, this yields the first\textit{Fixed-depth Size-Hierarchy Theorem for the uniform version of this class: our results imply that for any fixed d, the class \mathcal{C_{d,k} of functions that have uniform AC^0[\oplus] formulas of depth d and size n^k form an infinite hierarchy} _2 solving the \delta-coin problem, which may be of independent interest} .
Revised:  In particular, this yields the first\textit{ for the uniform version of this class: our results imply that for any fixed d, the class \mathcal{C_{d,k} of functions that have uniform AC^0[\oplus] formulas of depth d and size n^k form an infinite hierarchy} _2 solving the \delta-coin problem, which may be of independent interest} .
Edit intent: clarity
Original:  In particular, this yields the first\textit{Fixed-depth Size-Hierarchy Theorem for the uniform version of this class: our results imply that for any fixed d, the class \mathcal{C_{d,k} of functions that have uniform AC^0[\oplus] formulas of depth d and size n^k form an infinite hierarchy} _2 solving the \delta-coin problem, which may be of independent interest} .
Revised:  In particular, this yields the first\textit{Fixed-depth Size-Hierarchy Theorem _{d,k} of functions that have uniform AC^0[\oplus] formulas of depth d and size n^k form an infinite hierarchy} _2 solving the \delta-coin problem, which may be of independent interest} .
Edit intent: clarity
Original:  Given a query video, the objective is to retrieve all associated videos, considering several types of association that range from duplicate videos to videos from the same incident.
Revised:  Given a query video, the objective is to retrieve all associated videos, considering several types of associations that range from duplicate videos to videos from the same incident.
Edit intent: fluency
Original:  FIVR offers a single framework that contains as special cases several retrieval tasks  .
Revised:  FIVR offers a single framework that contains several retrieval tasks .
Edit intent: clarity
Original:  To address the benchmarking needs of all such tasks, we constructed and present a large-scale annotated video dataset, which we call FIVR-200K  and it comprises 225,960 videos.
Revised:  To address the benchmarking needs of all such tasks, we construct and present a large-scale annotated video dataset, which we call FIVR-200K and it comprises 225,960 videos.
Edit intent: fluency
Original:  To address the benchmarking needs of all such tasks, we constructed and present a large-scale annotated video dataset, which we call FIVR-200K  and it comprises 225,960 videos.
Revised:  To address the benchmarking needs of all such tasks, we constructed and present a large-scale annotated video dataset, which we call FIVR-200K , and it comprises 225,960 videos.
Edit intent: fluency