wanyu/IteraTeR_v2 huggingface dataset:
Original:  Motivated by recent results relating synchronizing automata and primitive sets, we study the length of the shortest product of a primitive set having a column or a row with k positive entries (the k-RT ) . We prove that this value is at most linear w.r.t. the matrix size n for small k, while the problem is still open for synchronizing automata.
Revised:  Motivated by recent results relating synchronizing automata and primitive sets, we study the length of the shortest product of a primitive set having a column or a row with k positive entries (the k-RT ) . We prove that the k-RT is at most linear w.r.t. the matrix size n for small k, while the problem is still open for synchronizing automata.
Edit intent: clarity
Original: Complex networks can be modeled as a probabilistic graphical model, where the interactions between binary variables, "spins", on nodes are described by a coupling matrix that is inferred from observations.
Edit intent: coherence
Original:  The inverse statistical problem of finding direct interactions is difficult, especially for large systems, because of the exponential growth in the possible number of states and the possible number of networks .
Revised:  The inverse statistical problem of finding direct interactions in complex networks is difficult .
Edit intent: clarity
Original:  In the context of the experimental sciences, well-controlled perturbations can be applied to a system, shedding light on the internal structure of the network.
Revised:  In the context of the experimental sciences, well-controlled perturbations can be applied to a system, probing the internal structure of the network.
Edit intent: clarity
Original:  Therefore, we propose a method to improve the accuracy and efficiency of inference by iteratively applying perturbations to a network that are advantageous under a Bayesian framework.
Revised:  Therefore, we propose a general mathematical framework to study inference with iteratively applied perturbations to a network that are advantageous under a Bayesian framework.
Edit intent: clarity
Original:  We significantly improve the accuracy and efficiency of inference in medium-sized networks based on this strategy with a reasonable number of experimental queries .
Revised:  We significantly improve the accuracy and efficiency of inference from a reasonable number of experimental queries .
Edit intent: clarity
Original:  In the context of the experimental sciences, well-controlled perturbations can be applied to a system, probing the internal structure of the network .
Revised:  In the natural sciences, well-controlled perturbations can be applied to a system, probing the internal structure of the network .
Edit intent: clarity
Original:  Specifically , we study the problem of training game agents in service of the developmentprocesses of the game developers that design, build, and operate modern games.
Revised:  Specifically , we study the problem of training intelligent agents in service of the developmentprocesses of the game developers that design, build, and operate modern games.
Edit intent: clarity
Original:  The U.S. National Institute of Health continues to be a major funder of cited science.
Revised:  The U.S. National Institute of Health continues to be an important funder of cited science.
Edit intent: clarity
Original:  Taken together, these results indicate a continuous contribution of public science to private sector inventions.
Revised:  Taken together, these results indicate a continuous linkage of public science to private sector inventions.
Edit intent: clarity
Original:  However, training different models for  ensemble is not only difficult but also inefficient with respect to time or memory.
Revised:  However, training different models for the ensemble is not only difficult but also inefficient with respect to time or memory.
Edit intent: coherence
Original:  However, training different models for  ensemble is not only difficult but also inefficient with respect to time or memory.
Revised:  However, training different models for ensemble is not only difficult but also inefficient with respect to time and memory.
Edit intent: fluency
Original:  In this paper, we propose a novel framework that exploits multiple global descriptors to get an ensemble-like effect while it can be trained in an end-to-end manner.
Revised:  In this paper, we propose a novel framework that exploits multiple global descriptors to get an ensemble effect while it can be trained in an end-to-end manner.
Edit intent: clarity
Original:  In the benchmark evaluation, the proposed framework achieves the state-of-the-art performance on the CARS196, CUB200-2011, In-shop Clothes  and Stanford Online Products on image retrieval tasks by a large margin compared to competing approaches .
Revised:  In the benchmark evaluation, the proposed framework achieves the state-of-the-art performance on the CARS196, CUB200-2011, In-shop Clothes , and Stanford Online Products on image retrieval tasks by a large margin compared to competing approaches .
Edit intent: fluency
Original:  In the benchmark evaluation, the proposed framework achieves the state-of-the-art performance on the CARS196, CUB200-2011, In-shop Clothes  and Stanford Online Products on image retrieval tasks by a large margin compared to competing approaches .
Revised:  In the benchmark evaluation, the proposed framework achieves the state-of-the-art performance on the CARS196, CUB200-2011, In-shop Clothes and Stanford Online Products on image retrieval tasks .
Edit intent: clarity
Original:  A global system of various packet switching quantum and classical networks is called quantum internet, the internet in the future.
Revised:  The future internet will be a global system of various packet switching quantum and classical networks is called quantum internet, the internet in the future.
Edit intent: clarity
Original:  To pave the way to the future quantum internet, unified protocols that support the distribution of quantum messages within the quantum internet are necessary.
Revised:  To pave the way to the future quantum internet, unified protocols that support the distribution of quantum messages within it are necessary.
Edit intent: clarity
Original:  In particular, the creation of the logical process-to-process connections of qTCP is accomplished by a quantum version of the three-way handshake protocol.
Revised:  In particular, the creation of the logical process-to-process connections is accomplished by a quantum version of the three-way handshake protocol.
Edit intent: clarity
Original:  The future internet will be a global system of various packet switching quantum and classical networks and we call it quantum internet \emph{ .
Revised:  The future internet will be a global system of various packet switching quantum and classical networks and we call it \emph{ .
Edit intent: fluency
Original:  In particular, the creation of the logical process-to-process connections is accomplished by a quantum version of the three-way handshake protocol.
Revised:  In particular, the creation of logical process-to-process connections is accomplished by a quantum version of the three-way handshake protocol.
Edit intent: fluency
Original: The maximum independent set problem is a classical NP-complete problem in graph theory and has important practical applications in many domains.
Revised: The maximum independent set problem is a classical NP-complete problem in graph theory and has important applications in many domains.
Edit intent: clarity
Original: We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of semialgebraic sets given by Boolean formulas.
Revised: We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of semialgebraic sets given by Boolean formulas.
Edit intent: clarity
Original:  All previous algorithms proposed for this problem have doubly exponential complexity (and this is so for almost all input data) .
Revised:  All previous algorithms proposed for this problem have doubly exponential complexity .
Edit intent: clarity
Original: We present a scalable nonparametric Bayesian method to perform network reconstruction from observed functional behavior , that at the same time infers the communities present in the network.
Revised: We present a scalable nonparametric Bayesian method to perform network reconstruction from observed functional behavior that at the same time infers the communities present in the network.
Edit intent: fluency
Original:  We show that the joint reconstruction with community detection has a synergistic effect, where the edge correlations used to inform the existence of communities are inherently also used to improve the accuracy of the reconstruction , whichin turn can better inform the uncovering of communities.
Revised:  We show that the joint reconstruction with community detection has a synergistic effect, where the edge correlations used to inform the existence of communities are also inherently used to improve the accuracy of the reconstruction , whichin turn can better inform the uncovering of communities.
Edit intent: fluency
Original:  We show that the joint reconstruction with community detection has a synergistic effect, where the edge correlations used to inform the existence of communities are inherently also used to improve the accuracy of the reconstruction , whichin turn can better inform the uncovering of communities.
Revised:  We show that the joint reconstruction with community detection has a synergistic effect, where the edge correlations used to inform the existence of communities are inherently also used to improve the accuracy of the reconstruction which, in turn, can better inform the uncovering of communities.
Edit intent: fluency
Original:  We design a recursive predictor that computes future interference values at a given location by filtering measured interference at this location.
Revised:  We design a recursive predictor that forecasts future interference values at a given location by filtering measured interference at this location.
Edit intent: clarity
Original:  We design a recursive predictor that forecasts future interference values at a given location by filtering measured interference at this location.
Revised:  We design a recursive predictor that estimates future interference values at a given location by filtering measured interference at this location.
Edit intent: clarity
Original:  We design a recursive predictor that forecasts future interference values at a given location by filtering measured interference at this location.
Revised:  We design a recursive predictor that forecasts future interference values by filtering measured interference at this location.
Edit intent: clarity
Original:  We design a recursive predictor that forecasts future interference values at a given location by filtering measured interference at this location.
Revised:  We design a recursive predictor that forecasts future interference values at a given location by filtering measured interference at a given location.
Edit intent: clarity
Original:  The parametrization of the predictor is done offline by translating the autocorrelation of interference into an autoregressive moving average (ARMA) representation.
Revised:  The predictor's parameterization is done offline by translating the autocorrelation of interference into an autoregressive moving average (ARMA) representation.
Edit intent: clarity
Original:  Results show good performance in terms of accuracy between predicted and true values for relevant time horizons.
Revised:  Results show a good accuracy of predicted values versus true values for relevant time horizons.
Edit intent: clarity
Original:  Although the predictor is parametrized for the case of Poisson networks , Rayleigh fading, and fixed message lengths, a sensitivity analysis shows that it also works well in more general network scenarios.
Revised:  Although the predictor is parameterized for Poisson-distributed nodes , Rayleigh fading, and fixed message lengths, a sensitivity analysis shows that it also works well in more general network scenarios.
Edit intent: clarity
Original:  Although the predictor is parametrized for the case of Poisson networks , Rayleigh fading, and fixed message lengths, a sensitivity analysis shows that it also works well in more general network scenarios.
Revised:  Although the predictor is parametrized for the case of Poisson networks , Rayleigh fading, and fixed message lengths, a sensitivity analysis shows that it also tends to work well in more general network scenarios.
Edit intent: clarity
Original:  Numerical examples for underlay device-to-device communications and a common wireless sensor technology  illustrate its broad applicability.
Revised:  Numerical examples for underlay device-to-device communications , a common wireless sensor technology illustrate its broad applicability.
Edit intent: fluency
Original: Convergence failure and slow convergence rate are among the biggest challenges with solving the system of non-linear equations numerically.
Revised: Convergence failure and slow convergence rates are among the biggest challenges with solving the system of non-linear equations numerically.
Edit intent: fluency
Original:  Although mitigated, such issues still linger when using strictly small time steps sizes and unconditionally stable fully implicit schemes.
Revised:  Although mitigated, such issues still linger when using strictly small time steps and unconditionally stable fully implicit schemes.
Edit intent: clarity
Original:  The price that comes with applying strictly small time steps is the enormous computational load, especially in large-scale models.
Revised:  The price that comes with restricting time steps to small scales is the enormous computational load, especially in large-scale models.
Edit intent: clarity
Original:  To address this problem, we introduce a sequential local mesh refinement scheme in space-time domain that improves convergence rate and prevents convergence failure while not restricting the whole system to small time steps, thus boosting computational efficiency.
Revised:  To address this problem, we introduce a sequential local mesh refinement framework to optimize convergence rate and prevents convergence failure while not restricting the whole system to small time steps, thus boosting computational efficiency.
Edit intent: clarity
Original:  To address this problem, we introduce a sequential local mesh refinement scheme in space-time domain that improves convergence rate and prevents convergence failure while not restricting the whole system to small time steps, thus boosting computational efficiency.
Revised:  To address this problem, we introduce a sequential local mesh refinement scheme in space-time domain that improves convergence rate and prevent convergence failure, while not restricting the whole system to small time steps, thus boosting computational efficiency.
Edit intent: fluency
Original:  To address this problem, we introduce a sequential local mesh refinement scheme in space-time domain that improves convergence rate and prevents convergence failure while not restricting the whole system to small time steps, thus boosting computational efficiency.
Revised:  To address this problem, we introduce a sequential local mesh refinement scheme in space-time domain that improves convergence rate and prevents convergence failure while not restricting the whole system to small time steps, thus improving computational efficiency.
Edit intent: clarity
Original:  Starting by solving the coarsest mesh in space-time domain , the algorithm refines the domain in time at water saturation front to prevent convergence failure.
Revised:  Starting by solving the problem on the coarsest space-time domain , the algorithm refines the domain in time at water saturation front to prevent convergence failure.
Edit intent: clarity
Original:  Starting by solving the coarsest mesh in space-time domain , the algorithm refines the domain in time at water saturation front to prevent convergence failure.
Revised:  Starting by solving the coarsest mesh in space-time mesh , the algorithm refines the domain in time at water saturation front to prevent convergence failure.
Edit intent: clarity
Original:  It then deploys fine spatial mesh in regions with large saturation variation to compensate solution accuracy.
Revised:  It then deploys fine spatial grid in regions with large saturation variation to compensate solution accuracy.
Edit intent: clarity
Original:  It then deploys fine spatial mesh in regions with large saturation variation to compensate solution accuracy.
Revised:  It then deploys fine spatial mesh in regions with large saturation variation to assure solution accuracy.
Edit intent: clarity
Original:  After each refinement, the solution from the previous mesh is used to estimate  initial guess of  the current mesh for faster convergence.
Revised:  After each refinement, the solution from the previous mesh is used to estimate the initial guess of the current mesh for faster convergence.
Edit intent: fluency
Original:  After each refinement, the solution from the previous mesh is used to estimate  initial guess of  the current mesh for faster convergence.
Revised:  After each refinement, the solution from the previous mesh is used to estimate initial guess of unknowns on the current mesh for faster convergence.
Edit intent: clarity
Original:  We observe around 25 times speedup in the solution time by using our algorithm.
Revised:  We observe approximately 25 times speedup in the solution time by using our algorithm.
Edit intent: clarity
Original:  On the positive side, we present polynomial-time algorithms with approximation ratios 2\frac{e for machines with unrelated speeds, 3 for machines with uniform speeds, and 7/3 for restricted assignments on identical machines.
Revised:  On the positive side, we present polynomial-time algorithms with approximation ratios \frac{2e for machines with unrelated speeds, 3 for machines with uniform speeds, and 7/3 for restricted assignments on identical machines.
Edit intent: fluency
Original:  Jobs are required to be executed non-preemptively and in unison, in the sense that they occupy, during their execution, the same time interval over all the machines of the allocated set.
Revised:  In this setting, jobs are required to be executed non-preemptively and in unison, in the sense that they occupy, during their execution, the same time interval over all the machines of the allocated set.
Edit intent: clarity
Original:  Specifically, we introduce a general model of malleable job scheduling, where each machine has a (possibly different) speed for each job, and the processing time of a job j on a set of allocated machines S depends on the total speed of S for j.
Revised:  Specifically, we introduce a general model of malleable job scheduling, where each machine has a (possibly different) speed for each job, and the processing time of a job j on a set of allocated machines S depends on the total speed of S with respect to j.
Edit intent: clarity
Original:  Our algorithms are based on deterministic LP rounding and result in sparse schedules, in the sense that each machine shares at most one job with other machines.
Revised:  Our algorithms are based on deterministic LP rounding . They result in sparse schedules, in the sense that each machine shares at most one job with other machines.
Edit intent: coherence
Original: Anthropologists have long appreciated that single-layer networks are insufficient descriptions of human interactions---individuals are embedded in complex networks with dependencies.
Revised: Anthropologists have long appreciated that relationships between individuals cannot be described from observing a single domain, and that the structure across domains of interaction can have important effects on outcomes of interest (e.g., cooperation).1
Edit intent: clarity
Original:   Recent models of these processes show how ignoring layer interdependencies can lead one to miss why a layer formed the way it did, and/or draw erroneous conclusions .
Revised:  Recent models of these processes show how ignoring layer interdependencies can lead one to miss why a layer formed the way it did, and/or draw erroneous conclusions .6
Edit intent: fluency
Original:  Understanding the structuring processes that underlie multiplex networks will help understand increasingly rich datasets, which give better, richer, and more accurate pictures of social interactions.
Revised:  Understanding the structuring processes that underlie multiplex networks will help understand increasingly rich datasets, giving more accurate and complete pictures of social interactions.
Edit intent: clarity
Original:  Each UAV is constrained in its energy storage and wireless coverage, and it consumes most energy when flying to the top of the target area, leaving limited leftover energy for hovering at its deployed position and providing wireless coverage.
Revised:  Each UAV is constrained in its energy storage and wireless coverage, and it consumes most energy when flying to the top of the target area, leaving limited leftover energy for hovering at its deployed position and keeping wireless coverage.
Edit intent: clarity
Original:  The literature largely overlooks this sustainability issue of UAV network deploymentto prolong the UAV network's residual lifetime for providing wireless coverage , and we aim to maximize the minimum leftover energy storage among all  UAVs after their deployment.
Revised:  The literature largely overlooks this sustainability issue of UAV network deploymentto prolong the UAV network's residual lifetime for providing wireless coverage , and we aim to maximize the minimum leftover energy storage among all the UAVs after their deployment.
Edit intent: fluency
Original:  Moreover, when n  UAVs are dispatched from different initial locations, we first prove that any two UAVs  will not fly across each other in the flight as long as they have the same initial energy storage , and then design a fully polynomial time approximation scheme (FPTAS) of time complexity O( n \log 1{\epsilon} ) to arbitrarily approach the optimum with relative error \epsilon.
Revised:  Moreover, when n UAVs are dispatched from different initial locations, we first prove that any two UAVs will not fly across each other , and then design a fully polynomial time approximation scheme (FPTAS) of time complexity O( n \log 1{\epsilon} ) to arbitrarily approach the optimum with relative error \epsilon.
Edit intent: coherence
Original:  Moreover, when n  UAVs are dispatched from different initial locations, we first prove that any two UAVs  will not fly across each other in the flight as long as they have the same initial energy storage , and then design a fully polynomial time approximation scheme (FPTAS) of time complexity O( n \log 1{\epsilon} ) to arbitrarily approach the optimum with relative error \epsilon.
Revised:  Moreover, when n UAVs are dispatched from different initial locations, we first prove that any two UAVs will not fly across each other in the flight as long as they have the same initial energy storage , and then design an approximation algorithm of complexity n \log 1{\epsilon} ) to arbitrarily approach the optimum with relative error \epsilon.
Edit intent: clarity
Original:  Moreover, when n  UAVs are dispatched from different initial locations, we first prove that any two UAVs  will not fly across each other in the flight as long as they have the same initial energy storage , and then design a fully polynomial time approximation scheme (FPTAS) of time complexity O( n \log 1{\epsilon} ) to arbitrarily approach the optimum with relative error \epsilon.
Revised:  Moreover, when n UAVs are dispatched from different initial locations, we first prove that any two UAVs will not fly across each other in the flight as long as they have the same initial energy storage , and then design a fully polynomial time approximation scheme (FPTAS) of time complexity O( n \log 1{\epsilon} to arbitrarily approach the optimum with relative error \epsilon.
Edit intent: fluency