wanyu/IteraTeR_v2 huggingface dataset:
Original:  and depth O(\log N\cdot\mathrm{poly}(} \log ^{2\kappa_B) to }%DIFDELCMD < \widetilde{O}%%% (m_{B\log ^{2}n}  + n\log ^{4n\cdot\log^{5}\kappa_B), where \kappa_B is } , matrix B=D-M as above, outputs a spectral sparsifier of matrix-polynomial whose coefficients approximate component-wise the discretized p.d.f. }\hat{w} the condition number of the input SDDM matrix B.
Revised:  and depth O(\log N\cdot\mathrm{poly}(} \log ^{2\kappa_B) to }%DIFDELCMD < \widetilde{O}%%% (m_{B\log ^{2}n} n) + n\log ^{4n\cdot\log^{5}\kappa_B), where \kappa_B is } , matrix B=D-M as above, outputs a spectral sparsifier of matrix-polynomial whose coefficients approximate component-wise the discretized p.d.f. }\hat{w} the condition number of the input SDDM matrix B.
Edit intent: fluency
Original: When B is a dense Laplacian matrix , our result leads to the first nearly linear time algorithm for analyzing the long term behaviour of random walks induced by transition matrices of the form \sum_{i=0^{N}\gamma_{i}(D^{-1} M)^i, where \gamma is induced by MDBD and the random walk length N=\Theta(n)}  }\hspace{0pt} parallel SDD solver} .
Revised: When B is a dense Laplacian matrix , our result leads to the first nearly linear time algorithm for analyzing the long term behaviour of ^{N}\gamma_{i}(D^{-1} M)^i, where \gamma is induced by MDBD and the random walk length N=\Theta(n)} }\hspace{0pt} parallel SDD solver} .
Edit intent: clarity
Original: For "large" class C of continuous probability density functions (p.d.f.), we demonstrate that for every w\inC there is mixture of discrete Binomial distributions (MDBD) with T\geq N\phi_{w/\delta} distinct Binomial distributions B(\cdot,N) that \delta-approximates a discretized p.d.f. (i/N)\triangleq w(i/N)/[\ell=0^{N}w(\ell/N)] for all i\in[3:N-3], where w\geqx\in[0,1]|w(x)|.
Revised: For "large" class C of continuous probability density functions (p.d.f.), we demonstrate that for every w\inC there is mixture of discrete Binomial distributions (MDBD) with T\geq N\phi_{w/\delta} distinct Binomial distributions B(\cdot,N) that \delta-approximates a discretized p.d.f. (i/N)\triangleq w(i/N)/[\ell=0^{N}w(\ell/N)] for all i\in[3:N-3], where w\geqx\in[0,1]|w(x)|.
Edit intent: clarity
Original:  we prove this using a reduction from planar 3-sat that is based upon oriented-disc drawings.
Revised:  we prove thisusing a reduction from planar 3-sat that is based upon oriented-disc drawings.
Edit intent: fluency
Original:  we prove this using a reduction from planar 3-sat that is based upon oriented-disc drawings.
Revised:  we prove this using a reduction from planar 3-SAT that is based upon oriented-disc drawings.
Edit intent: clarity
Original:  Preliminary tests on a simple task show that the stochastic approximation of the gradient introduced in the algorithm does not seem to introduce too much noise in the trajectory, compared to maintaining the full gradient, and confirm the good performance and scalability of the Kalman-like version of NoBackTrack  .
Revised:  Small-scale experiments confirm the suitability of the approach, showing that the stochastic approximation of the gradient introduced in the algorithm does not seem to introduce too much noise in the trajectory, compared to maintaining the full gradient, and confirm the good performance and scalability of the Kalman-like version of NoBackTrack .
Edit intent: clarity
Original:  Preliminary tests on a simple task show that the stochastic approximation of the gradient introduced in the algorithm does not seem to introduce too much noise in the trajectory, compared to maintaining the full gradient, and confirm the good performance and scalability of the Kalman-like version of NoBackTrack  .
Revised:  Preliminary tests on a simple task show that the stochastic approximation of the gradient introduced in the algorithm is not detrimental to learning. In particular, the Kalman-like version of NoBackTrack .
Edit intent: clarity
Original:  This approach yields polynomial upper bounds on the runtime of an Iterated version of the GA on 2-SAT problem and on a family of Set Cover problems proposed by E. Balas.
Revised:  This approach yields polynomial upper bounds on the runtime of EAs on 2-SAT problem and on a family of Set Cover problems proposed by E. Balas.
Edit intent: clarity
Original: As the traffic load in cellular networks grows rapidly, future generation cellular networks will involve multiple radio access technologies (RATs) over different frequency bands.
Revised: As the traffic load in cellular networks accelerates, emerging services will make use of multiple radio access technologies (RATs) over different frequency bands.
Edit intent: clarity
Original: As the traffic load in cellular networks grows rapidly, future generation cellular networks will involve multiple radio access technologies (RATs) over different frequency bands.
Revised: As the traffic load in cellular networks grows rapidly, future generation cellular networks will involve multiple radio access technologies (RATs) over both licensed and unlicensed frequency bands.
Edit intent: clarity
Original:  This paper studies the spectrum allocation problem in  heterogeneous networks (HetNets) with multiple RATs over different bands using the average packet sojourn time as performance metric.
Revised:  This paper studies the spectrum allocation problem in such heterogeneous networks (HetNets) with multiple RATs over different bands using the average packet sojourn time as performance metric.
Edit intent: clarity
Original:  The framework developed recently in 1%DIFDELCMD < ] %%% is generalized to incorporate multiple RATs.
Revised:  The framework developed recently in %DIFDELCMD < ] %%% is generalized to incorporate multiple RATs.
Edit intent: clarity
Original:  In contrast to the licensed band, the queueing model for the unlicensed band captures the lower spectral efficiency, reliability, and additional delay due to contention and/or listen-before-talk requirements  .
Revised:  In contrast to the licensed band, the queueing model for the unlicensed band to capture its lower spectral efficiency, reliability, and additional delay due to contention and/or listen-before-talk requirements .
Edit intent: clarity
Original:  In contrast to the licensed band, the queueing model for the unlicensed band captures the lower spectral efficiency, reliability, and additional delay due to contention and/or listen-before-talk requirements  .
Revised:  In contrast to the licensed band, the queueing model for the unlicensed band captures the lower spectral efficiency, reliability, and additional delay due to contention and/or listen-before-talk requirements in contrast to licensed bands .
Edit intent: coherence
Original:  Under mild assumptions, we formulate the spectrum allocation problem as a convex optimization problem.
Revised:  Under mild assumptions, the spectrum allocation problem as a convex optimization problem.
Edit intent: clarity
Original:  Solving this problem gives an effective and  efficient solution for  user association and spectrum allocation over multiple RATs.
Revised:  Solving this problem gives an effective and efficient solution for both user association and spectrum allocation over multiple RATs.
Edit intent: clarity
Original:  Simulation results show that in the heavy-traffic regime, the proposed scheme significantly outperforms both orthogonal spectrum allocation and full-frequency-reuse allocation .
Revised:  Simulation results show that in the heavy-traffic regime, the proposed scheme significantly outperforms both orthogonal and full-frequency-reuse allocation .
Edit intent: clarity
Original:  Simulation results show that in the heavy-traffic regime, the proposed scheme significantly outperforms both orthogonal spectrum allocation and full-frequency-reuse allocation .
Revised:  Simulation results show that in the heavy-traffic regime, the proposed scheme significantly outperforms both orthogonal spectrum allocation and full-frequency-reuse allocations .
Edit intent: clarity
Original:  In addition, the optimal solution to the optimization problem matches the intuition that users with relatively high traffic demand are mostly assigned to  licensed spectrum, while those with low traffic demand and less interference are assigned to  unlicensed spectrum.
Revised:  In addition, the solution to the optimization problem matches the intuition that users with relatively high traffic demand are mostly assigned to licensed spectrum, while those with low traffic demand and less interference are assigned to unlicensed spectrum.
Edit intent: clarity
Original:  In addition, the optimal solution to the optimization problem matches the intuition that users with relatively high traffic demand are mostly assigned to  licensed spectrum, while those with low traffic demand and less interference are assigned to  unlicensed spectrum.
Revised:  In addition, the optimal solution to the optimization problem matches the intuition that users with relatively high traffic demand are mostly assigned to the licensed spectrum, while those with low traffic demand and less interference are assigned to unlicensed spectrum.
Edit intent: fluency
Original:  In addition, the optimal solution to the optimization problem matches the intuition that users with relatively high traffic demand are mostly assigned to  licensed spectrum, while those with low traffic demand and less interference are assigned to  unlicensed spectrum.
Revised:  In addition, the optimal solution to the optimization problem matches the intuition that users with relatively high traffic demand are mostly assigned to licensed spectrum, while those with low traffic demand and less interference are assigned to the unlicensed spectrum.
Edit intent: fluency
Original: As the traffic load in cellular networksaccelerates, emerging services will make use of multiple radio access technologies (RATs) over both licensed and unlicensed frequency bands.
Revised: In future networks, an operator may employ a wide range of access points using diverse radio access technologies (RATs) over both licensed and unlicensed frequency bands.
Edit intent: clarity
Original: As the traffic load in cellular networksaccelerates, emerging services will make use of multiple radio access technologies (RATs) over both licensed and unlicensed frequency bands.
Revised: As the traffic load in cellular networksaccelerates, emerging services will make use of multiple radio access technologies (RATs) over multiple licensed and unlicensed frequency bands.
Edit intent: clarity
Original:  This paper studies the spectrum allocation problem in such heterogeneous networks (HetNets)on a relatively slow timescale , so that joint allocation across many cells is practical .
Revised:  This paper studies centralized user association and spectrum allocation across many access points in such a heterogeneous network (HetNet). For practical reasons, such centralized control is likely to be on a much slower timescale than frame transmissions .
Edit intent: clarity
Original:  A queueing model is introduced for the unlicensed band to capture its lower spectral efficiency, reliability, and additional delay due to contention and/or listen-before-talk requirements in contrast to licensed bands.
Revised:  A queueing model is introduced to capture the lower spectral efficiency, reliability, and additional delay due to contention and/or listen-before-talk requirements in contrast to licensed bands.
Edit intent: clarity
Original:  A queueing model is introduced for the unlicensed band to capture its lower spectral efficiency, reliability, and additional delay due to contention and/or listen-before-talk requirements in contrast to licensed bands.
Revised:  A queueing model is introduced for the unlicensed band to capture its lower spectral efficiency, reliability, and additional delays of data transmission over the unlicensed bands due to contention and/or listen-before-talk requirements in contrast to licensed bands.
Edit intent: clarity
Original:  Simulation results show that in the heavy-traffic regime, the proposed scheme significantly outperforms both orthogonal and full-frequency-reuse allocations .
Revised:  Simulation results show that the proposed schemes significantly outperform orthogonal and full-frequency-reuse allocations .
Edit intent: clarity
Original:  For practical reasons, such centralized control is likely to be on a much slower timescale than frame transmissions .
Revised:  Such centralized control is likely to be on a much slower timescale than frame transmissions .
Edit intent: clarity
Original:  We also provide instructions on how to make use of GHOST in existing software packages, together with a case study which demonstrating the applicability and performance of GHOST as a component within a larger software stack.
Revised:  We also provide instructions on how to make use of GHOST in existing software packages, together with a case study which demonstrates the applicability and performance of GHOST as a component within a larger software stack.
Edit intent: fluency
Original:  Here we  give tight lower bounds for the size  such solution sets when the input graph is either a interval graph, or a unit interval graph, or a (bipartite) permutation graph or a cograph .
Revised:  Here we study the case of interval graphs, unit interval graphs, (bipartite) permutation graphs and cographs. For these classes of graphs we give tight lower bounds for the size such solution sets when the input graph is either a interval graph, or a unit interval graph, or a (bipartite) permutation graph or a cograph .
Edit intent: coherence
Original:  Here we  give tight lower bounds for the size  such solution sets when the input graph is either a interval graph, or a unit interval graph, or a (bipartite) permutation graph or a cograph .
Revised:  Here we give tight lower bounds for the size of such solution sets when the input graph is either a interval graph, or a unit interval graph, or a (bipartite) permutation graph or a cograph .
Edit intent: fluency
Original:  While such lower bounds for the general class of graphs are in logarithmic order (or order of graph) , the improved bounds in these special classes are of the order of either quadratic root or linear in terms of number of vertices.
Revised:  While such lower bounds for the general class of graphs are in logarithmic order , the improved bounds in these special classes are of the order of either quadratic root or linear in terms of number of vertices.
Edit intent: coherence
Original:  Using the connection between linear equivalence for chip-firing and for rotor-routing, we prove that the number of rotor-router unicycle-orbits equals the order of the Picard group.
Revised:  Using the connection between linear equivalence for chip-firing and for rotor-routing, we give a simple proof for the fact that the number of rotor-router unicycle-orbits equals the order of the Picard group.
Edit intent: clarity
Original:  In spite of large uncertainty due to the small size of most published empirical landscapes, the inferred landscapes have similar structure in similar biological systems.
Revised:  In spite of uncertainty due to the small size of most published empirical landscapes, the inferred landscapes have similar structure in similar biological systems.
Edit intent: clarity
Original:  A better understanding of variation of landscape structure across species and environments is thus necessary to understand and predict how populations  adapt.
Revised:  A better understanding of variation of landscape structure across species and environments is thus necessary to understand and predict how populations will adapt.
Edit intent: fluency
Original:  An increasing number of experiments access the properties of fitness landscapes by identifying mutations, constructing genotypes with combinations of these mutations, and measuring  fitness of these genotypes.
Revised:  An increasing number of experiments investigates the properties of fitness landscapes by identifying mutations, constructing genotypes with combinations of these mutations, and measuring fitness of these genotypes.
Edit intent: clarity
Original:  An increasing number of experiments access the properties of fitness landscapes by identifying mutations, constructing genotypes with combinations of these mutations, and measuring  fitness of these genotypes.
Revised:  An increasing number of experiments access the properties of fitness landscapes by identifying mutations, constructing genotypes with combinations of these mutations, and measuring the fitness of these genotypes.
Edit intent: fluency
Original:  Yet these empirical landscapes represent a very small sample of the vast space of all possible genotypes, and this sample is  biased by the protocol used to identify mutations.
Revised:  Yet these empirical landscapes represent a very small sample of the vast space of all possible genotypes, and this sample is often biased by the protocol used to identify mutations.
Edit intent: clarity
Original:  Here we develop a rigorous and flexible statistical framework based on Approximate Bayesian Computation to address these concerns, and use this  framework to fit a broad class of phenotypic fitness models (including Fisher's model) to 24 empirical landscapes representing 9 diverse biological systems.
Revised:  Here we develop a rigorous statistical framework based on Approximate Bayesian Computation to address these concerns, and use this framework to fit a broad class of phenotypic fitness models (including Fisher's model) to 24 empirical landscapes representing 9 diverse biological systems.
Edit intent: clarity
Original:  Here we develop a rigorous and flexible statistical framework based on Approximate Bayesian Computation to address these concerns, and use this  framework to fit a broad class of phenotypic fitness models (including Fisher's model) to 24 empirical landscapes representing 9 diverse biological systems.
Revised:  Here we develop a rigorous and flexible statistical framework based on Approximate Bayesian Computation to address these concerns, and use this flexible framework to fit a broad class of phenotypic fitness models (including Fisher's model) to 24 empirical landscapes representing 9 diverse biological systems.
Edit intent: fluency
Original:  In most cases, including notably the landscapes of drug resistance, Fisher's model is not able to explain the structure of empirical landscapes and patterns of epistasis .
Revised:  More precisely, although Fisher's model is not able to explain the structure of empirical landscapes and patterns of epistasis .
Edit intent: coherence
Original:  In most cases, including notably the landscapes of drug resistance, Fisher's model is not able to explain the structure of empirical landscapes and patterns of epistasis .
Revised:  In most cases, including notably the landscapes of drug resistance, Fisher's model was able to explain the structure of empirical landscapes and patterns of epistasis .
Edit intent: coherence
Original: The current epidemic of Ebola Virus Disease (EVD)  in West Africa is the largest ever recorded,  a fundamental shift in the epidemiology of Ebola with unprecedented spatiotemporal complexity.
Revised: The current epidemic of Ebola Virus Disease (EVD) in West Africa was the largest ever recorded, a fundamental shift in the epidemiology of Ebola with unprecedented spatiotemporal complexity.
Edit intent: fluency
Original: The current epidemic of Ebola Virus Disease (EVD)  in West Africa is the largest ever recorded,  a fundamental shift in the epidemiology of Ebola with unprecedented spatiotemporal complexity.
Revised: The current epidemic of Ebola Virus Disease (EVD) in West Africa is the largest ever recorded, representing a fundamental shift in the epidemiology of Ebola with unprecedented spatiotemporal complexity.
Edit intent: clarity
Original: The current epidemic of Ebola Virus Disease (EVD)  in West Africa is the largest ever recorded,  a fundamental shift in the epidemiology of Ebola with unprecedented spatiotemporal complexity.
Revised: The current epidemic of Ebola Virus Disease (EVD) in West Africa is the largest ever recorded, a fundamental shift in Ebola epidemiology with unprecedented spatiotemporal complexity.
Edit intent: clarity
Original:  The  model structure and intervention analysis presented here provide information that can be used by policymakers and public health officials to help guide planning and response efforts for this and future epidemics.
Revised:  The model structure and intervention analysis provides information that can be used by policymakers and public health officials to help guide planning and response efforts for this and future epidemics.
Edit intent: clarity
Original:  The  model structure and intervention analysis presented here provide information that can be used by policymakers and public health officials to help guide planning and response efforts for this and future epidemics.
Revised:  The model structure and intervention analysis presented here provide information that can be used by public health policymakers to assist planning and response efforts for this and future epidemics.
Edit intent: clarity
Original:  The  model structure and intervention analysis presented here provide information that can be used by policymakers and public health officials to help guide planning and response efforts for this and future epidemics.
Revised:  The model structure and intervention analysis presented here provide information that can be used by policymakers and public health officials to help guide planning and response efforts for future epidemics.
Edit intent: clarity
Original:  The multiplex networks that we consider combine transcription factor co-targeting, microRNA co-targeting, protein-protein interaction and gene co-expression networks.
Revised:  The multi-networks that we consider combine transcription factor co-targeting, microRNA co-targeting, protein-protein interaction and gene co-expression networks.
Edit intent: clarity
Original:  To this end we applied a consensus clustering algorithm to the single-layer partitions obtained using state of art community detection methods , combined with a filtering preprocessing of the individual networks .
Revised:  To this end we applied a consensus clustering algorithm based on state of art community detection methods , combined with a filtering preprocessing of the individual networks .
Edit intent: clarity
Original:  To this end we applied a consensus clustering algorithm to the single-layer partitions obtained using state of art community detection methods , combined with a filtering preprocessing of the individual networks .
Revised:  To this end we applied a consensus clustering algorithm to the single-layer partitions obtained using state of art community detection methods .
Edit intent: clarity
Original:  Some of them were already known oncogenes while a few are new and represent the major result of our analysis .
Revised:  Some of them were already known oncogenes while a few are new .
Edit intent: clarity
Original:  The combination of the different layers of information allowed us to extract from the multiplex indications on the regulatory pattern and the functional role of both the already known oncogenes and the new candidate driver genes.
Revised:  The combination of the different layers of information allowed us to extract from the multi-network indications on the regulatory pattern and the functional role of both the already known oncogenes and the new candidate driver genes.
Edit intent: clarity
Original:  The combination of the different layers of information allowed us to extract from the multiplex indications on the regulatory pattern and the functional role of both the already known oncogenes and the new candidate driver genes.
Revised:  The combination of the different layers of information allowed us to extract from the multiplex indications on the regulatory pattern and functional role of both the already known oncogenes and the new candidate driver genes.
Edit intent: fluency