wanyu/IteraTeR_v2 huggingface dataset:
Original:  In the usual setting where the matrix to approximate has n columns with n%DIFDELCMD < \le %%% m, we provide a certificate of size m n, which can be computed in O(m^\omega D{m}) operations and which allows us to verify an approximant basis by a Monte Carlo algorithm with cost bound O(m^\omega + mD ).
Revised:  %DIFDELCMD < \le %%% m, we provide a certificate of size m n, which can be computed in O(m^\omega D{m}) operations and which allows us to verify an approximant basis by a Monte Carlo algorithm with cost bound O(m^\omega + mD ).
Edit intent: coherence
Original:  In the usual setting where the matrix to approximate has n columns with n%DIFDELCMD < \le %%% m, we provide a certificate of size m n, which can be computed in O(m^\omega D{m}) operations and which allows us to verify an approximant basis by a Monte Carlo algorithm with cost bound O(m^\omega + mD ).
Revised:  In the usual setting where the matrix to approximate has n columns with n%DIFDELCMD < \le %%% m, we provide a certificate of size m n, which can be computed in O(m^\omega D{m}) operations and which allows us to verify an approximant basis by a Monte Carlo algorithm with cost bound O(m^\omega + m D ).
Edit intent: fluency
Original: We first investigate static properties of opening and closing auctions such as typical auction volume relative to daily volume and order value distributions .
Revised: We first investigate the evolution of opening and closing auctions such as typical auction volume relative to daily volume and order value distributions .
Edit intent: clarity
Original: In a previous paper [Adcock & Huybrechs, 2016] we described the numerical properties of function approximation using frames, i.e.  complete systems that are generally redundant but provide infinite representations with coefficients of bounded norm.
Revised: In a previous paper [Adcock & Huybrechs, 2016] we described the numerical properties of function approximation using frames, i.e. \ complete systems that are generally redundant but provide infinite representations with coefficients of bounded norm.
Edit intent: fluency
Original:  Overall, we show that numerical function approximation using truncated frames leads to highly accurate approximations in spite of having to solve an ill-conditioned system of equations.
Revised:  Overall, we demonstrate that numerical function approximation using truncated frames leads to highly accurate approximations in spite of having to solve an ill-conditioned system of equations.
Edit intent: coherence
Original:  Overall, we show that numerical function approximation using truncated frames leads to highly accurate approximations in spite of having to solve an ill-conditioned system of equations.
Revised:  Overall, we show that numerical function approximation using truncated frames leads to highly accurate approximations in spite of having to solve ill-conditioned system of equations.
Edit intent: fluency
Original:  Overall, we show that numerical function approximation using truncated frames leads to highly accurate approximations in spite of having to solve an ill-conditioned system of equations.
Revised:  Overall, we show that numerical function approximation using truncated frames leads to highly accurate approximations in spite of having to solve an ill-conditioned systems of equations.
Edit intent: fluency
Original:  We showed that, in spite of extreme ill-conditioning, a regularized projection onto a finite truncated frame can provide accuracy up to order \epsilon, where \epsilon is an arbitrarily small threshold.
Revised:  We showed that, in spite of said ill-conditioning, a regularized projection onto a finite truncated frame can provide accuracy up to order \epsilon, where \epsilon is an arbitrarily small threshold.
Edit intent: clarity
Original:  We showed that, in spite of extreme ill-conditioning, a regularized projection onto a finite truncated frame can provide accuracy up to order \epsilon, where \epsilon is an arbitrarily small threshold.
Revised:  We showed that, in spite of extreme ill-conditioning, approximations with regularization may still provide accuracy up to order \epsilon, where \epsilon is an arbitrarily small threshold.
Edit intent: clarity
Original:  Here, we generalize the setting in two ways.
Revised:  Here, we generalize that setting in two ways.
Edit intent: fluency
Original:  First, we assume information or samples from f from a wide class of linear operators acting on f, rather than inner products with the frame elements.
Revised:  We assume information or samples from f from a wide class of linear operators acting on f, rather than inner products with the frame elements.
Edit intent: coherence
Original:  Overall, we demonstrate that numerical function approximation using truncated frames leads to highly accurate approximations in spite of having to solve ill-conditioned systems of equations .
Revised:  Overall, we demonstrate that numerical function approximation using redundant representations may lead to highly accurate approximations in spite of having to solve ill-conditioned systems of equations .
Edit intent: clarity
Original: We discuss a statistical model of evolution of wealth distribution , growing inequality and economic stratification in macro-economic scale.
Revised: We discuss a statistical model of evolution of wealth distribution in a macro-economic scale.
Edit intent: clarity
Original:  Evolution is driven by multiplicative stochastic fluctuations governed by the law of proportionate growth as well as by direct interactions between individuals and interactions between the private and public sectors.
Revised:  Evolution is driven by multiplicative stochastic fluctuations governed by the law of proportionate growth and interactions between the private and public sectors.
Edit intent: clarity
Original:  We observe such a multimodal pattern in empirical data on wealth distribution for  urban areas of China.
Revised:  We observe such a multimodal pattern in empirical data on wealth distribution for the population in urban areas of China.
Edit intent: clarity
Original:  Our novel algorithm to accurately determine this posterior requires significant fewer discrete model evaluations than traditional Monte Carlo methods.
Revised:  Our novel algorithm to accurately determine this posterior requires significantly fewer discrete model evaluations than traditional Monte Carlo methods.
Edit intent: fluency
Original: In this paper we propose and study the problem of trajectory-driven influential billboard placement: given a set of billboards U (each associated with a location and a cost), a database of trajectories T and a budget L, the goal is to find a set of billboards within the budget so that the placed ad can influence the largest number of trajectories.
Revised: In this paper we propose and study the problem of trajectory-driven influential billboard placement: given a set of billboards U (each with a location and a cost), a database of trajectories T and a budget L, the goal is to find a set of billboards within the budget so that the placed ad can influence the largest number of trajectories.
Edit intent: clarity
Original: In this paper we propose and study the problem of trajectory-driven influential billboard placement: given a set of billboards U (each associated with a location and a cost), a database of trajectories T and a budget L, the goal is to find a set of billboards within the budget so that the placed ad can influence the largest number of trajectories.
Revised: In this paper we propose and study the problem of trajectory-driven influential billboard placement: given a set of billboards U (each associated with a location and a cost), a database of trajectories T and a budget L, find a set of billboards within the budget so that the placed ad can influence the largest number of trajectories.
Edit intent: clarity
Original: In this paper we propose and study the problem of trajectory-driven influential billboard placement: given a set of billboards U (each associated with a location and a cost), a database of trajectories T and a budget L, the goal is to find a set of billboards within the budget so that the placed ad can influence the largest number of trajectories.
Revised: In this paper we propose and study the problem of trajectory-driven influential billboard placement: given a set of billboards U (each associated with a location and a cost), a database of trajectories T and a budget L, the goal is to find a set of billboards within the budget to influence the largest number of trajectories.
Edit intent: coherence
Original:  One core challenge is that multiple billboards have influence overlap on trajectories and it is critical to identify and reduce the influence overlap .
Revised:  One core challenge is to identify and reduce the influence overlap .
Edit intent: clarity
Original:  Two more constraints on top of this challenge, i.e., the budget constraint and non-uniform costs associated with each billboard, make this optimization problem more intricate .
Revised:  Two more constraints on top of this challenge, i.e., the budget constraint into consideration .
Edit intent: clarity
Original:  We show that this problem is NP-hard and propose an enumeration based algorithm with (1-1/e)
Revised:  We show that this problem is NP-hard and present an enumeration based algorithm with (1-1/e)
Edit intent: clarity
Original:  approximation ratio and O( | \mathcal{T|\cdot|} U| ^{5 . By exploiting the locality property of billboards  influence,
Revised:  approximation ratio and O( | |\cdot|} U| ^{5 . By exploiting the locality property of billboards influence,
Edit intent: coherence
Original:  approximation ratio and O( | \mathcal{T|\cdot|} U| ^{5 . By exploiting the locality property of billboards  influence,
Revised:  approximation ratio and O( | \mathcal{T|\cdot|} U| ^{5 . By exploiting the locality property of billboards ' influence,
Edit intent: fluency
Original:  we propose a partition-based framework %DIFDELCMD < \psel%%% .%DIFDELCMD < \psel %%%  partitions U into a set of small clusters,
Revised:  we propose a partition-based framework %DIFDELCMD < \psel%%% %DIFDELCMD < \psel %%% partitions U into a set of small clusters,
Edit intent: fluency
Original:  computes the locally influential billboards for each cluster, and merges the local billboards to generate the globally influential billboards of U. As a result, the computation cost is reduced to O(|\mathcal{T|\cdot|C_m|^5), where |C_m| is the cardinality of the largest partition in U. Furthermore, }  we propose a %DIFDELCMD < \bbsel %%%  method to further prune billboards with low marginal influence ;
Revised:  computes the locally influential billboards for each cluster, and merges them to generate the globally influential billboards of U. As a result, the computation cost is reduced to O(|\mathcal{T|\cdot|C_m|^5), where |C_m| is the cardinality of the largest partition in U. Furthermore, } we propose a %DIFDELCMD < \bbsel %%% method to further prune billboards with low marginal influence ;
Edit intent: clarity
Original:  computes the locally influential billboards for each cluster, and merges the local billboards to generate the globally influential billboards of U. As a result, the computation cost is reduced to O(|\mathcal{T|\cdot|C_m|^5), where |C_m| is the cardinality of the largest partition in U. Furthermore, }  we propose a %DIFDELCMD < \bbsel %%%  method to further prune billboards with low marginal influence ;
Revised:  computes the locally influential billboards for each cluster, and merges the local billboards to generate the globally influential billboards of U. As a result, the computation cost |\cdot|C_m|^5), where |C_m| is the cardinality of the largest partition in U. Furthermore, } we propose a %DIFDELCMD < \bbsel %%% method to further prune billboards with low marginal influence ;
Edit intent: clarity
Original:  computes the locally influential billboards for each cluster, and merges the local billboards to generate the globally influential billboards of U. As a result, the computation cost is reduced to O(|\mathcal{T|\cdot|C_m|^5), where |C_m| is the cardinality of the largest partition in U. Furthermore, }  we propose a %DIFDELCMD < \bbsel %%%  method to further prune billboards with low marginal influence ;
Revised:  computes the locally influential billboards for each cluster, and merges the local billboards to generate the globally influential billboards of U. As a result, the computation cost is reduced to O(|\mathcal{T|\cdot|C_m|^5), where |C_m| is the cardinality of the largest partition in U. Furthermore, } we propose a %DIFDELCMD < \bbsel %%% method to further prune billboards with low marginal influence 
Edit intent: fluency
Original: %DIFDELCMD < \bbsel %%% significantly reduces the practical cost of%DIFDELCMD < \psel %%%  while achieving the same approximation ratio as %DIFDELCMD < \psel%%%  . Experiments on real datasets show that our method achieves high influence and efficiency .
Revised: %DIFDELCMD < \bbsel %%% %DIFDELCMD < \psel %%% while achieving the same approximation ratio as %DIFDELCMD < \psel%%% . Experiments on real datasets show that our method achieves high influence and efficiency .
Edit intent: clarity
Original: %DIFDELCMD < \bbsel %%% significantly reduces the practical cost of%DIFDELCMD < \psel %%%  while achieving the same approximation ratio as %DIFDELCMD < \psel%%%  . Experiments on real datasets show that our method achieves high influence and efficiency .
Revised: %DIFDELCMD < \bbsel %%% significantly reduces the practical cost of%DIFDELCMD < \psel %%% , while achieving the same approximation ratio as %DIFDELCMD < \psel%%% . Experiments on real datasets show that our method achieves high influence and efficiency .
Edit intent: fluency
Original: %DIFDELCMD < \bbsel %%% significantly reduces the practical cost of%DIFDELCMD < \psel %%%  while achieving the same approximation ratio as %DIFDELCMD < \psel%%%  . Experiments on real datasets show that our method achieves high influence and efficiency .
Revised: %DIFDELCMD < \bbsel %%% significantly reduces the practical cost of%DIFDELCMD < \psel %%% while achieving the same approximation ratio as %DIFDELCMD < \psel%%% . Experiments on real datasets verify the efficiency and effectiveness of our methods .
Edit intent: clarity
Original: Compression of deep neural networks (DNNs) for memory- and computation-efficient compact feature representations becomes a critical problem particularly for deployment of DNNs on resource-limited platforms.
Edit intent: coherence
Original:  In this paper, we investigate lossy compression of DNNs by weight quantization and lossless source coding for memory-efficient inference .
Revised:  In this paper, we investigate lossy compression of DNNs by weight quantization and lossless source coding for memory-efficient deployment .
Edit intent: clarity
Original:  Our experimental results show that the proposed universal DNN compression scheme achieves compression ratios of 124.80, 47.10 and 42.46 for LeNet5, 32-layer ResNet  and AlexNet , respectively.
Revised:  Our experimental results show that the proposed universal DNN compression scheme compresses the 32-layer ResNet and AlexNet , respectively.
Edit intent: clarity
Original:  The main focus of this paper is on enhancement of two types of game-theoretic learning algorithms: log linear learning and reinforcement learning.
Revised:  The main focus of this paper is on enhancement of two types of game-theoretic learning algorithms: log-linear learning and reinforcement learning.
Edit intent: fluency
Original:  Each algorithm proposed in this paper, relaxes and imposes different assumptions to fit a class of MAS problems . Numerical experiments are also conducted to verify each algorithm's robustness and performance.
Revised:  Each algorithm proposed in this paper, relaxes and imposes different assumptions to fit a class of MAS problems . Numerical experiments are conducted to verify each algorithm's robustness and performance.
Edit intent: clarity
Original:  We show that, for Max-IP with two sets of n vectors from \{0,1\}^{d}, there is an n^{2 - \Omega(1)} time \Omega(d)-additive-approximating algorithm, and we show this is conditionally optimal, as such an o(d)-approximating algorithm would refute SETH  . Last, we revisit the hardness of solving Max-IP exactly for vectors with integer entries.
Revised:  We show that, for Max-IP with two sets of n vectors from \{0,1\}^{d}, there is an n^{2 - \Omega(1)} time \Omega(d)-additive-approximating algorithm, and this is conditionally optimal, as such an o(d)-approximating algorithm would refute SETH . Last, we revisit the hardness of solving Max-IP exactly for vectors with integer entries.
Edit intent: fluency
Original: In the past four decades, the notion of quantum polynomial-time computability has been realized by the theoretical models of quantum Turing machines and quantum circuits.
Revised: In the past four decades, the notion of quantum polynomial-time computability has been modeled by quantum Turing machines and quantum circuits.
Edit intent: clarity
Original: In the past four decades, the notion of quantum polynomial-time computability has been realized by the theoretical models of quantum Turing machines and quantum circuits.
Revised: In the past four decades, the notion of quantum polynomial-time computability has been realized by the theoretical models of quantum Turing machines as well as quantum circuits.
Edit intent: clarity
Original:  For quantum functions mapping finite-dimensional Hilbert spaces to themselves, we present such a schematic definition, composed of a small set of initial quantum functions and a few construction rules that dictate how to build a new quantum function from the existing quantum functions.
Revised:  For quantum functions , which map finite-dimensional Hilbert spaces to themselves, we present such a schematic definition, composed of a small set of initial quantum functions and a few construction rules that dictate how to build a new quantum function from the existing quantum functions.
Edit intent: fluency
Original:  Here, we seek a third model, which is a quantum analogue of the schematic (inductive or constructive) definition of (primitive) recursive functions.
Revised:  This paper seeks the third model, which is a quantum analogue of the schematic (inductive or constructive) definition of (primitive) recursive functions.
Edit intent: coherence
Original:  For quantum functions , which map finite-dimensional Hilbert spaces to themselves, we present such a schematic definition, composed of a small set of initial quantum functions and a few construction rules that dictate how to build a new quantum function from the existing quantum functions .
Revised:  For quantum functions mapping finite-dimensional Hilbert spaces to themselves, we present such a schematic definition, composed of a small set of initial quantum functions and a few construction rules that dictate how to build a new quantum function from the existing quantum functions .
Edit intent: coherence
Original:  For quantum functions , which map finite-dimensional Hilbert spaces to themselves, we present such a schematic definition, composed of a small set of initial quantum functions and a few construction rules that dictate how to build a new quantum function from the existing quantum functions .
Revised:  For quantum functions , which map finite-dimensional Hilbert spaces to themselves, we present such a schematic definition, composed of a small set of initial quantum functions and a few construction rules that dictate how to build a new quantum function from the existing ones .
Edit intent: clarity
Original:  We prove that our schematic definition precisely characterizes all functions that can be computable with high success probabilities on well-formed quantum Turing machines in polynomial time or equivalently, uniform families of polynomial-size quantum circuits.
Revised:  We prove that our schematic definition precisely characterizes all functions that can be computable with high success probabilities on well-formed quantum Turing machines in polynomial time , or equivalently uniform families of polynomial-size quantum circuits.
Edit intent: fluency
Original:  Our new approach can further open a door to the descriptional complexity of other functionsand to the theory of higher-type quantum functionals  .
Revised:  Our new approach can further open a door to the descriptional complexity of quantum functions, to the theory of higher-type quantum functionals .
Edit intent: clarity
Original: The article shows a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation.
Revised: This article explores a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation.
Edit intent: clarity
Original:  A pairwise comparisons matrix with elements from  alo-group is investigated.
Revised:  A pairwise comparisons matrix with elements from an alo-group is investigated.
Edit intent: fluency
Original:  This approach allows for generalization of the previous results.
Revised:  This approach allows for a generalization of previous results.
Edit intent: fluency
Original:  A numerical example focused on main results is presented.
Revised:  A numerical example is presented.
Edit intent: clarity
Original: Motivated by observations in DNA data of the human cytomegalovirus, we study the dynamics and the maintenance of diversity in a hierarchical model of a two-type parasite population distributed over its (infected) hosts.
Revised: Motivated by observations in DNA data of the human cytomegalovirus, we study the dynamics and the maintenance of diversity in a hierarchical model of a two-type parasite population distributed over its hosts.
Edit intent: clarity
Original:  The parasite is assumed to be capable to persist in its host and to reinfect other hosts , and balancing selection is assumed to maintain diversity within hosts.
Revised:  The parasite is assumed to be capable to persist in its host and to reinfect other hosts and balancing selection is assumed to maintain diversity within hosts.
Edit intent: fluency
Original: Motivated by observations in DNA data of the human cytomegalovirus , we study the dynamics and the maintenance of diversity in a hierarchical model of a two-type parasite population distributed over its hosts.
Revised: Inspired by DNA data of the human cytomegalovirus , we study the dynamics and the maintenance of diversity in a hierarchical model of a two-type parasite population distributed over its hosts.
Edit intent: clarity
Original: Motivated by observations in DNA data of the human cytomegalovirus , we study the dynamics and the maintenance of diversity in a hierarchical model of a two-type parasite population distributed over its hosts.
Revised: Motivated by observations in DNA data of the human cytomegalovirus we propose a model of a two-type parasite population distributed over its hosts.
Edit intent: clarity
Original:  The parasite is assumed to be capable to persist in its host  and to reinfect other hosts and balancing selection is assumed to maintain diversity within hosts .
Revised:  The parasite is capable to persist in its host and to reinfect other hosts and balancing selection is assumed to maintain diversity within hosts .
Edit intent: fluency
Original:  The parasite is assumed to be capable to persist in its host  and to reinfect other hosts and balancing selection is assumed to maintain diversity within hosts .
Revised:  The parasite is assumed to be capable to persist in its host and to reinfect other hosts and balancing selection is assumed .
Edit intent: clarity