wanyu/IteraTeR_v2 huggingface dataset:
Original: We consider the following general scheduling problem : there are m identical machines and n jobs all released at time 0. Each job j has a processing time p_j , and an arbitrary non-decreasing  function f_j that specifies the cost incurred for j, for each possible completion time.
Revised: We consider the following general scheduling problem : there are m identical machines and n jobs all released at time 0. Each job j has a processing time p_j , and an arbitrary non-decreasing cost function f_j that specifies the cost incurred for j, for each possible completion time.
Edit intent: fluency
Original: We consider the following general scheduling problem : there are m identical machines and n jobs all released at time 0. Each job j has a processing time p_j , and an arbitrary non-decreasing  function f_j that specifies the cost incurred for j, for each possible completion time.
Revised: We consider the following general scheduling problem : there are m identical machines and n jobs all released at time 0. Each job j has a processing time p_j , and an arbitrary non-decreasing function f_j of its completion time.
Edit intent: clarity
Original:  We give the first O(1) approximation algorithm for this problem, improving upon the  O(\log \log nP) bound due to Moseley (2019).
Revised:  We give the first O(1) approximation for the problem, improving upon the O(\log \log nP) bound due to Moseley (2019).
Edit intent: clarity
Original:  We give the first O(1) approximation algorithm for this problem, improving upon the  O(\log \log nP) bound due to Moseley (2019).
Revised:  We give the first O(1) approximation algorithm for this problem, improving upon the previous O(\log \log nP) bound due to Moseley (2019).
Edit intent: clarity
Original:  We show that Spherical Discrepancy is APX-hard and develop a multiplicative weights-based algorithm that achieves nearly optimal worst-case error bounds  .
Revised:  We show that Spherical Discrepancy is APX-hard and develop a multiplicative weights-based algorithm that achieves optimal worst-case error bounds .
Edit intent: clarity
Original:  Finally, we show how to modify our algorithm to solve a natural version of the Koml \'o%DIFDELCMD < }%%% s problem for the spherical setting .
Revised:  Finally, we show how to modify our algorithm to solve a natural version of the Koml %DIFDELCMD < }%%% s problem for the spherical setting .
Edit intent: clarity
Original: In this note an error estimate in the L^2-norm of order O(h^{k+1{2}}) is proven for a finite element method for a linearised model of inviscid incompressible flow .
Revised: In this note an error estimate in the L^2-norm of order O(h^{k+1{2}}) .
Edit intent: coherence
Original:  We also prove error estimates of the same order for the pressure error in the L^2-norm.
Revised:  We also prove error estimates for the pressure error in the L^2-norm.
Edit intent: clarity
Original:  We introduce an intersection type assignment system for Moggi's computational lambda-calculus, where a generic monad T is considered, and provide a concrete model of the calculus via a filter model construction .
Revised:  We introduce an intersection type assignment system for Moggi's computational lambda-calculus, where a generic monad T is considered, and provide models of the calculus via a filter model construction .
Edit intent: clarity
Original:  Most  works stand by the view of non-cooperative-game theoretical framework with the shared reward approach, i.e., each agent is assigned a shared global reward directly.
Revised:  Most of works stand by the view of non-cooperative-game theoretical framework with the shared reward approach, i.e., each agent is assigned a shared global reward directly.
Edit intent: clarity
Original:  Most  works stand by the view of non-cooperative-game theoretical framework with the shared reward approach, i.e., each agent is assigned a shared global reward directly.
Revised:  Most works stand by the view of non-cooperative-game theoretical framework with the shared reward approach, i.e., each agent being assigned a shared global reward directly.
Edit intent: clarity
Original:  This, however, may give each agent an inaccurate feedback on his contribution to the group.
Revised:  This, however, may give each agent an inaccurate feedback on its contribution to the group.
Edit intent: clarity
Original:  In this paper, we introduce a cooperative-game theoretical framework and extend it to the finite-horizon case.
Revised:  In this paper, we introduce a cooperative-game theoretical framework and extend it to the infinite-horizon case.
Edit intent: fluency
Original:  Based on this framework, we propose an algorithm called Shapley Q-value policy gradient (SQPG) to learn a local reward approach  that can distribute the cumulative global reward fairly, reflecting each agent's own contribution in contrast to the shared reward approach.
Revised:  Based on this framework, we propose a local reward approach that can distribute the cumulative global reward fairly, reflecting each agent's own contribution in contrast to the shared reward approach.
Edit intent: coherence
Original:  Based on this framework, we propose an algorithm called Shapley Q-value policy gradient (SQPG) to learn a local reward approach  that can distribute the cumulative global reward fairly, reflecting each agent's own contribution in contrast to the shared reward approach.
Revised:  Based on this framework, we propose an algorithm called Shapley Q-value policy gradient (SQPG) to learn a local reward approach that can distribute the cumulative global rewards fairly, reflecting each agent's own contribution in contrast to the shared reward approach.
Edit intent: fluency
Original:  In the experiments, our algorithm shows better convergence than the baselines  .
Revised:  In the experiments, SQPG shows the better performance than the baselines .
Edit intent: clarity
Original: Cooperative game is a critical research area in  multi-agent reinforcement learning (MARL).
Revised: Cooperative game is a critical research area in the multi-agent reinforcement learning (MARL).
Edit intent: fluency
Original:  Global reward game is a subclass of cooperative games, where all agents aim to maximize cumulative global rewards . Credit assignment is an important problem studied in the global reward game.
Revised:  Global reward game is a subclass of cooperative games, where all agents aim to maximize the global reward . Credit assignment is an important problem studied in the global reward game.
Edit intent: clarity
Original:  Most of works stand by the view of non-cooperative-game theoretical framework with the shared reward approach, i.e., each agent being assigned a shared global reward directly.
Revised:  Most of previous works stood by the view of non-cooperative-game theoretical framework with the shared reward approach, i.e., each agent being assigned a shared global reward directly.
Edit intent: clarity
Original:  This, however, may give each agent an inaccurate feedback on its contribution to the group .
Revised:  This, however, may give each agent an inaccurate reward on its contribution to the group .
Edit intent: clarity
Original:  We show that our proposed framework is a superset of the global reward game . Based on this framework, we propose a local reward approach called Shapley Q-value that can distribute the cumulative global rewards fairly , reflecting each agent's own contribution in contrast to the shared reward approach.
Revised:  We show that our proposed framework is a superset of global reward game . Based on this framework, we propose a local reward approach called Shapley Q-value that can distribute the cumulative global rewards fairly , reflecting each agent's own contribution in contrast to the shared reward approach.
Edit intent: fluency
Original:  We show that our proposed framework is a superset of the global reward game . Based on this framework, we propose a local reward approach called Shapley Q-value that can distribute the cumulative global rewards fairly , reflecting each agent's own contribution in contrast to the shared reward approach.
Revised:  We show that our proposed framework is a superset of the global reward game , and ii) propose a local reward approach called Shapley Q-value that can distribute the cumulative global rewards fairly , reflecting each agent's own contribution in contrast to the shared reward approach.
Edit intent: coherence
Original:  We show that our proposed framework is a superset of the global reward game . Based on this framework, we propose a local reward approach called Shapley Q-value that can distribute the cumulative global rewards fairly , reflecting each agent's own contribution in contrast to the shared reward approach.
Revised:  We show that our proposed framework is a superset of the global reward game . Based on this framework, we propose a local reward approach called Shapley Q-value . Shapley Q-value is able to distribute the global reward , reflecting each agent's own contribution in contrast to the shared reward approach.
Edit intent: clarity
Original:  We evaluate SQPG on Cooperative Navigation, Prey-and-Predator and Traffic Junction, compared with  MADDPG, COMA, Independent A2C and Independent DDPG . In the experiments, SQPG shows the better performance than the baselines.
Revised:  We evaluate SQPG on Cooperative Navigation, Prey-and-Predator and Traffic Junction, compared with MADDPG, COMA, Independent DDPG and Independent A2C . In the experiments, SQPG shows the better performance than the baselines.
Edit intent: fluency
Original:  Extensive work has been done in this field to overcome these limits, yet no general remedy that keeps all the positive features of the discrete model along with an arbitrary Poisson's ratio has been developed.
Edit intent: coherence
Original:  The real shrinking of the Poisson's ratio limit is therefore less severe compared to that which is theoretically derived.
Revised:  The real shrinking of the Poisson's ratio limit is less severe compared to that which is theoretically derived.
Edit intent: coherence
Original: In the analysis of metastable diffusion processes, Transition Path Theory (TPT) provides a way to quantify the probability of observing a given transition between two disjoint metastable subsets of state space.
Revised: Transition path theory (TPT) provides a way to quantify the probability of observing a given transition between two disjoint metastable subsets of state space.
Edit intent: clarity
Original:  Our main result proves that when the network is a tree formed according to the preferential attachment model ~ BarabasiA99, with high probability, the process stabilizes in a correct majority  .
Revised:  Our main result proves that when the network is a tree formed according to the preferential attachment model BarabasiA99, with high probability, the process stabilizes in a correct majority .
Edit intent: fluency
Original:  Both algorithms are based on the approximation of the theoretical solutions by neural networks, the latter being characterized by their architecture and a set of parameters.
Revised:  Both algorithms are based on approximations of the theoretical solutions by neural networks, the latter being characterized by their architecture and a set of parameters.
Edit intent: fluency
Original:  We provide a mathematical proof of the convergence of the algorithm , and we analyze rigorously the approximation by controlling the different sources of error.
Revised:  We provide a mathematical proof of the convergence of the approximation scheme , and we analyze rigorously the approximation by controlling the different sources of error.
Edit intent: clarity
Original:  Specifically, we relax a notion of distribution privacy  by generalizing it to divergence, and investigate local obfuscation mechanisms that provide the divergence distribution privacy.
Revised:  Specifically, we relax a notion of distribution privacy by generalizing it to divergence, and propose local obfuscation mechanisms that provide the divergence distribution privacy.
Edit intent: clarity
Original:  Specifically, we relax a notion of distribution privacy  by generalizing it to divergence, and investigate local obfuscation mechanisms that provide the divergence distribution privacy.
Revised:  Specifically, we relax a notion of distribution privacy by generalizing it to divergence, and investigate local obfuscation mechanisms that provide divergence distribution privacy.
Edit intent: fluency
Original:  In addition, our framework naturally incorporates spatial mixing properties to obtain linear expected running time . Using this new technique, we give the currently best perfect sampling algorithms for colorings in bounded degree graphs and in graphs with sub-exponential neighborhood growth .
Revised:  In addition, our framework naturally incorporates spatial mixing properties to obtain linear expected running time . Using this new technique, we give the currently best perfect samplers for colorings and for monomer-dimer models in such graphs .
Edit intent: clarity
Original: In this paper, we propose an efficient high order semi-Lagrangian (SL) discontinuous Galerkin (DG) method for solving linear convection-diffusion-reaction equations.
Revised: In this paper, we propose an efficient high order semi-Lagrangian (SL) discontinuous Galerkin (DG) method for solving linear convection-diffusion equations.
Edit intent: clarity
Original:  while the diffusion are discretized by local DG (LDG) method and are integrated along characteristics by implicit Runge-Kutta methods together with source terms.
Revised:  while the diffusion term is discretized by the local DG (LDG) method and are integrated along characteristics by implicit Runge-Kutta methods together with source terms.
Edit intent: fluency
Original:  while the diffusion are discretized by local DG (LDG) method and are integrated along characteristics by implicit Runge-Kutta methods together with source terms.
Revised:  while the diffusion are discretized by local DG (LDG) method and integrated along characteristics by implicit Runge-Kutta methods together with source terms.
Edit intent: fluency
Original:  The proposed method is named the `SLDG-LDG' method , which enjoy many attractive features of the DG and SL methods.
Revised:  The proposed method is named the `SLDG-LDG' method and enjoys many attractive features of the DG and SL methods.
Edit intent: coherence
Original: Social media are vulnerable to deceptive social bots, which can impersonate humans to amplify misinformation and manipulate opinions.
Revised: Social media , the modern marketplace of ideas, is vulnerable to manipulation. Deceptive inauthentic actors impersonate humans to amplify misinformation and manipulate opinions.
Edit intent: clarity
Original: Social media are vulnerable to deceptive social bots, which can impersonate humans to amplify misinformation and manipulate opinions.
Revised: Social media are vulnerable to deceptive social bots, which can impersonate humans to amplify misinformation and influence public opinions.
Edit intent: clarity
Original:  Little is known about the large-scale consequences of such pollution operations .
Revised:  Little is known about the large-scale consequences of such operations, due to the ethical challenges posed by online experiments that manipulate human behavior .
Edit intent: clarity
Original:  Here we introduce an agent-based model of information spreading with quality preference and limited individual attentionto evaluate the impact of different strategies that bots can exploit to pollute the network and degrade the overall quality of the information ecosystem.
Revised:  Here we introduce a model of information spreading with quality preference and limited individual attentionto evaluate the impact of different strategies that bots can exploit to pollute the network and degrade the overall quality of the information ecosystem.
Edit intent: clarity
Original:  Here we introduce an agent-based model of information spreading with quality preference and limited individual attentionto evaluate the impact of different strategies that bots can exploit to pollute the network and degrade the overall quality of the information ecosystem.
Revised:  Here we introduce an agent-based model of information spreading where agents prefer quality information but have limited attention. We evaluate the impact of different strategies that bots can exploit to pollute the network and degrade the overall quality of the information ecosystem.
Edit intent: clarity
Original:  Here we introduce an agent-based model of information spreading with quality preference and limited individual attentionto evaluate the impact of different strategies that bots can exploit to pollute the network and degrade the overall quality of the information ecosystem.
Revised:  Here we introduce an agent-based model of information spreading with quality preference and limited individual attentionto evaluate the impact of manipulation strategies aimed at degrading the overall quality of the information ecosystem.
Edit intent: clarity
Original:   We find that penetrating a critical fraction of the network is more important than generating attention-grabbing content and that targeting random users is more damaging than targeting hub nodes.
Revised:  We find that infiltrating a critical fraction of the network is more important than generating attention-grabbing content and that targeting random users is more damaging than targeting hub nodes.
Edit intent: fluency
Original:   We find that penetrating a critical fraction of the network is more important than generating attention-grabbing content and that targeting random users is more damaging than targeting hub nodes.
Revised:  We find that penetrating a critical fraction of the network is more damaging than generating attention-grabbing content and that targeting random users is more damaging than targeting hub nodes.
Edit intent: clarity
Original: Quantum Teleportation is the key communication functionality of the Quantum Internet, allowing the ``transmission'' of qubits without either the physical transfer of the particle storing the qubit or the violation of the quantum mechanical principles.
Revised: Quantum Teleportation is the key communication functionality of the Quantum Internet, allowing the "transmission' of qubits without either the physical transfer of the particle storing the qubit or the violation of the quantum mechanical principles.
Edit intent: fluency
Original: In this paper, we propose an end to end joint radio and virtual network function (VNF ) resource allocation for next-generation networks providing different types of services with different requirements in term of latency and data rate.
Revised: In this paper, we propose an end to end joint radio and virtual network function (VNF ) resource allocation for next generation networks providing different types of services with different requirements in term of latency and data rate.
Edit intent: fluency
Original: In this paper, we propose an end to end joint radio and virtual network function (VNF ) resource allocation for next-generation networks providing different types of services with different requirements in term of latency and data rate.
Revised: In this paper, we propose an end to end joint radio and virtual network function (VNF ) resource allocation for next-generation networks providing different types of services with different requirements in terms of latency and data rate.
Edit intent: fluency
Original:  We consider both the access and core parts of the network  and formulate a novel optimization problem whose aim is to perform the radio resource allocation jointly with VNF embedding, scheduling, and resource allocation such that the network cost, defined as the consumed energy and the number of utilized network servers, is minimized.
Revised:  We consider both the access and core parts of the network , and formulate a novel optimization problem whose aim is to perform the radio resource allocation jointly with VNF embedding, scheduling, and resource allocation such that the network cost, defined as the consumed energy and the number of utilized network servers, is minimized.
Edit intent: fluency
Original:  We consider both the access and core parts of the network  and formulate a novel optimization problem whose aim is to perform the radio resource allocation jointly with VNF embedding, scheduling, and resource allocation such that the network cost, defined as the consumed energy and the number of utilized network servers, is minimized.
Revised:  We consider both the access and core parts of the network and formulate a novel optimization problem whose aim is to perform the radio resource allocation jointly with virtual network function (VNF) embedding, scheduling, and resource allocation such that the network cost, defined as the consumed energy and the number of utilized network servers, is minimized.
Edit intent: clarity
Original:  The proposed optimization problem is non-convex, NP-hard, and mathematically intractable, and hence, we use an alternative search method (ASM) to decouple the main problem into some sub-problems of lower complexity.
Revised:  The proposed optimization problem is non-convex, NP-hard, and mathematically intractable, and hence, we adopt the alternative search method (ASM) to decouple the main problem into some sub-problems of lower complexity.
Edit intent: clarity
Original:  We propose a novel heuristic algorithm for embedding and scheduling of VNFs by proposing a novel admission control (AC) algorithm.
Revised:  Moreover, w propose a novel heuristic algorithm for embedding and scheduling of VNFs by proposing a novel admission control (AC) algorithm.
Edit intent: coherence
Original:  We compare the performance of the proposed algorithm with a greedy-based solution in terms of the acceptance ratio and the number of active servers.
Revised:  Then, we compare the performance of the proposed algorithm with a greedy-based solution in terms of the acceptance ratio and the number of active servers.
Edit intent: coherence
Original: In this paper, we propose an end to end joint radio and network function virtualization (NFV) resource allocation for next generation networks providing different types of services with different requirements in terms of latency and data rate.
Revised: In this paper, we propose an end to end radio and network function virtualization (NFV) resource allocation for next generation networks providing different types of services with different requirements in terms of latency and data rate.
Edit intent: clarity
Original:  The proposed optimization problem is non-convex, NP-hard, and mathematically intractable, and hence, we adopt the alternative search method (ASM) to decouple the main problem into some sub-problems of lower complexity .
Revised:  The proposed optimization problem is non-convex, NP-hard, and mathematically intractable, and hence, we adopt the alternative search method (ASM) to decouple the main problem into low complex subproblems .
Edit intent: clarity
Original:  Moreover, w propose a novel heuristic algorithm for embedding and scheduling of VNFs by proposing a novel admission control (AC) algorithm.
Revised:  Moreover, we propose a novel heuristic algorithm for embedding and scheduling of VNFs by proposing a novel admission control (AC) algorithm.
Edit intent: fluency
Original:  Moreover, w propose a novel heuristic algorithm for embedding and scheduling of VNFs by proposing a novel admission control (AC) algorithm.
Revised:  Moreover, w propose a novel heuristic algorithm for NFV resource allocation by proposing a novel admission control (AC) algorithm.
Edit intent: clarity
Original:  Moreover, w propose a novel heuristic algorithm for embedding and scheduling of VNFs by proposing a novel admission control (AC) algorithm.
Revised:  Moreover, w propose a novel heuristic algorithm for embedding and scheduling of VNFs by proposing a novel admission control algorithm.
Edit intent: clarity
Original:  Our simulation results show that the proposed heuristic algorithm outperforms the conventional ones by approximately 8\% .
Revised:  Our simulation results show that the proposed heuristic algorithm outperforms the conventional ones by approximately 8\% 
Edit intent: fluency