wanyu/IteraTeR_v2 huggingface dataset:
Original: In this paper, we propose a novel resource management scheme that jointly allocates the transmit power and network function virtualization (NFV) resources in a centralized radio access network (C-RAN) architectureconsisting of several RRHs and a BBU pool.
Revised: In this paper, we propose a novel resource management scheme that jointly allocates the transmission power and computational resources in a centralized radio access network (C-RAN) architectureconsisting of several RRHs and a BBU pool.
Edit intent: clarity
Original:  The BBU pool is connected to a set of NFV-enabled nodes (including the multi-access%DIFDELCMD < \mobile %%% edge computing (MEC)-enabled node) to which the requested tasks of user equipments (UEs) are offloaded.
Revised:  The BBU pool is connected to a set of %DIFDELCMD < \mobile %%% edge computing (MEC)-enabled node) to which the requested tasks of user equipments (UEs) are offloaded.
Edit intent: clarity
Original:  The BBU pool is connected to a set of NFV-enabled nodes (including the multi-access%DIFDELCMD < \mobile %%% edge computing (MEC)-enabled node) to which the requested tasks of user equipments (UEs) are offloaded.
Revised:  The BBU pool is connected to a set of NFV-enabled nodes (including the multi-access%DIFDELCMD < \mobile %%% computing nodes to which the requested tasks of user equipments (UEs) are offloaded.
Edit intent: clarity
Original:  The BBU pool is connected to a set of NFV-enabled nodes (including the multi-access%DIFDELCMD < \mobile %%% edge computing (MEC)-enabled node) to which the requested tasks of user equipments (UEs) are offloaded.
Revised:  The BBU pool is connected to a set of NFV-enabled nodes (including the multi-access%DIFDELCMD < \mobile %%% edge computing (MEC)-enabled node) to which the requested tasks of different users are offloaded.
Edit intent: clarity
Original:  We formulate an optimization problem taking into account the transmission, execution, and propagation delays of each task  with the aim to allocate the transmission power in radio and computational resources in nodes such that the user's maximum tolerable latency is satisfied.
Revised:  The optimization problem takes the transmission, execution, and propagation delays of each task with the aim to allocate the transmission power in radio and computational resources in nodes such that the user's maximum tolerable latency is satisfied.
Edit intent: clarity
Original:  We formulate an optimization problem taking into account the transmission, execution, and propagation delays of each task  with the aim to allocate the transmission power in radio and computational resources in nodes such that the user's maximum tolerable latency is satisfied.
Revised:  We formulate an optimization problem taking into account the transmission, execution, and propagation delays of each task into account, with the aim to allocate the transmission power in radio and computational resources in nodes such that the user's maximum tolerable latency is satisfied.
Edit intent: clarity
Original:  We formulate an optimization problem taking into account the transmission, execution, and propagation delays of each task  with the aim to allocate the transmission power in radio and computational resources in nodes such that the user's maximum tolerable latency is satisfied.
Revised:  We formulate an optimization problem taking into account the transmission, execution, and propagation delays of each task with the aim to allocate the transmission power and computational resources in nodes such that the user's maximum tolerable latency is satisfied.
Edit intent: clarity
Original:  We formulate an optimization problem taking into account the transmission, execution, and propagation delays of each task  with the aim to allocate the transmission power in radio and computational resources in nodes such that the user's maximum tolerable latency is satisfied.
Revised:  We formulate an optimization problem taking into account the transmission, execution, and propagation delays of each task with the aim to allocate the transmission power in radio and computational resources such that the user's maximum tolerable latency is satisfied.
Edit intent: clarity
Original:  Since the proposed optimization problem is highly non-convex, we adopt the alternate search method (ASM) to achieve a sub-optimal solution.
Revised:  Since the optimization problem is highly non-convex, we adopt the alternate search method (ASM) to achieve a sub-optimal solution.
Edit intent: clarity
Original:  We also propose a new admission control mechanism for finding the set of tasks that can be served by the available resources.
Revised:  We also propose an admission control mechanism for finding the set of tasks that can be served by the available resources.
Edit intent: clarity
Original:  Furthermore, a disjoint method that separately allocates the transmission power and the computational resources are proposed as the baseline of comparison.
Revised:  Furthermore, a disjoint method that separately allocates the transmission power and the computational resources is proposed as the baseline of comparison.
Edit intent: fluency
Original: In this paper, we propose a novel resource management scheme that jointly allocates the transmission power and computational resources in a centralized radio access network architecture.
Revised: In this paper, we propose a novel resource management scheme that jointly allocates the transmit power and computational resources in a centralized radio access network architecture.
Edit intent: fluency
Original:  The optimization problem takes the transmission, execution, and propagation delays of each task into account, with the aim to allocate the transmission power and computational resources such that the user's maximum tolerable latency is satisfied.
Revised:  The optimization problem takes the transmission, execution, and propagation latencies of each task into account, with the aim to allocate the transmission power and computational resources such that the user's maximum tolerable latency is satisfied.
Edit intent: clarity
Original:  The optimization problem takes the transmission, execution, and propagation delays of each task into account, with the aim to allocate the transmission power and computational resources such that the user's maximum tolerable latency is satisfied.
Revised:  The optimization problem takes the transmission, execution, and propagation delays of each task , into account. We aim to allocate the transmission power and computational resources such that the user's maximum tolerable latency is satisfied.
Edit intent: coherence
Original:  The optimization problem takes the transmission, execution, and propagation delays of each task into account, with the aim to allocate the transmission power and computational resources such that the user's maximum tolerable latency is satisfied.
Revised:  The optimization problem takes the transmission, execution, and propagation delays of each task into account, with the aim to allocate the transmit power and computational resources such that the user's maximum tolerable latency is satisfied.
Edit intent: fluency
Original:  The optimization problem takes the transmission, execution, and propagation delays of each task into account, with the aim to allocate the transmission power and computational resources such that the user's maximum tolerable latency is satisfied.
Revised:  The optimization problem takes the transmission, execution, and propagation delays of each task into account, with the aim to allocate the transmission power and computational resources such that the maximum acceptable latency of each task is satisfied.
Edit intent: clarity
Original:  Since the optimization problem is highly non-convex, we adopt the alternate search method (ASM) to divide it into smaller subproblems.
Revised:  Since the optimization problem is non-convex, we adopt the alternate search method (ASM) to divide it into smaller subproblems.
Edit intent: clarity
Original:  Since the optimization problem is highly non-convex, we adopt the alternate search method (ASM) to divide it into smaller subproblems.
Revised:  Since the optimization problem is highly non-convex, we divide it into smaller subproblems.
Edit intent: clarity
Original:  A heuristic algorithm is proposed to jointly manage the allocated computational resources and placement of the tasks derived by ASM . We also propose an admission control mechanism for finding the set of tasksthat can be served by the available resources .
Revised:  A heuristic algorithm is proposed to jointly manage computational resources and placement of the tasks derived by ASM . We also propose an admission control mechanism for finding the set of tasksthat can be served by the available resources .
Edit intent: clarity
Original:  A heuristic algorithm is proposed to jointly manage the allocated computational resources and placement of the tasks derived by ASM . We also propose an admission control mechanism for finding the set of tasksthat can be served by the available resources .
Revised:  A heuristic algorithm is proposed to jointly manage the allocated computational resources and task placement . We also propose an admission control mechanism for finding the set of tasksthat can be served by the available resources .
Edit intent: clarity
Original:  A heuristic algorithm is proposed to jointly manage the allocated computational resources and placement of the tasks derived by ASM . We also propose an admission control mechanism for finding the set of tasksthat can be served by the available resources .
Revised:  A heuristic algorithm is proposed to jointly manage the allocated computational resources and placement of the tasks derived by ASM . We also propose a feasibility analysis that finds a feasible subset of tasks .
Edit intent: clarity
Original:  Furthermore, a disjoint method that separately allocates the transmission power and the computational resources is proposed as the baseline of comparison.
Revised:  Furthermore, a disjoint method that separately allocates the transmit power and the computational resources is proposed as the baseline of comparison.
Edit intent: fluency
Original:  The optimal solution of the optimization problem is also derived based on exhaustive search over offloading decisions and utilizing Karush-Kuhn-Tucker optimality conditions.
Revised:  The optimal solution of the optimization problem is also derived based on exhaustive search over task placement decisions and utilizing Karush-Kuhn-Tucker optimality conditions.
Edit intent: clarity
Original:  Our results indicate that traveling waves facilitate learning of distant and indirectly connected network-paths when combined with a reward-based local synaptic plasticity rule.
Revised:  Our results indicate that traveling waves facilitate learning of distant and indirectly connected network-paths when combined with a reward-dependent local synaptic plasticity rule.
Edit intent: clarity
Original:  We  demonstrate that traveling waves expedite finding the shortest paths and learning nonlinear input/output-mapping, such as the XOR function.
Revised:  We also demonstrate that traveling waves expedite finding the shortest paths and learning nonlinear input/output-mapping, such as the XOR function.
Edit intent: coherence
Original: In this paper we analyze a simple  method (EIG1) for the problem of matrix alignment, consisting in aligning their leading eigenvectors: given  A and B, we compute v_1 and v'_1 two leading eigenvectors of A and B .
Revised: In this paper we analyze a simple method (EIG1) for the problem of matrix alignment, consisting in aligning their leading eigenvectors: given two matrices A and B, we compute v_1 and v'_1 two leading eigenvectors of A and B .
Edit intent: clarity
Original: In this paper we analyze a simple  method (EIG1) for the problem of matrix alignment, consisting in aligning their leading eigenvectors: given  A and B, we compute v_1 and v'_1 two leading eigenvectors of A and B .
Revised: In this paper we analyze a simple method (EIG1) for the problem of matrix alignment, consisting in aligning their leading eigenvectors: given A and B, we compute v_1 and v'_1 two corresponding leading eigenvectors .
Edit intent: clarity
Original:  The algorithm returns a permutation%DIFDELCMD < \Pi %%% \pi such that the rank of the coordinate%DIFDELCMD < \Pi%%% \pi (i) in v_1 is the rank of the coordinate i in v'_1 (up to the sign of v'_1)  .
Revised:  The algorithm returns %DIFDELCMD < \Pi %%% \pi such that the rank of the coordinate%DIFDELCMD < \Pi%%% \pi (i) in v_1 is the rank of the coordinate i in v'_1 (up to the sign of v'_1) .
Edit intent: clarity
Original:  The algorithm returns a permutation%DIFDELCMD < \Pi %%% \pi such that the rank of the coordinate%DIFDELCMD < \Pi%%% \pi (i) in v_1 is the rank of the coordinate i in v'_1 (up to the sign of v'_1)  .
Revised:  The algorithm returns a permutation%DIFDELCMD < \Pi %%% \pi such that the rank of %DIFDELCMD < \Pi%%% \pi (i) in v_1 is the rank of the coordinate i in v'_1 (up to the sign of v'_1) .
Edit intent: fluency
Original:  The algorithm returns a permutation%DIFDELCMD < \Pi %%% \pi such that the rank of the coordinate%DIFDELCMD < \Pi%%% \pi (i) in v_1 is the rank of the coordinate i in v'_1 (up to the sign of v'_1)  .
Revised:  The algorithm returns a permutation%DIFDELCMD < \Pi %%% \pi such that the rank of the coordinate%DIFDELCMD < \Pi%%% \pi (i) in v_1 and that of coordinate i in v'_1 (up to the sign of v'_1) .
Edit intent: clarity
Original:  We show the following 0-1 law: under the condition \sigma N^{7/6+\epsilon} \to 0 , the EIG1 method recovers all but a vanishing part of the underlying permutation \Pi.
Revised:  We show the following 0-1 law: under the condition \sigma N^{7/6+\epsilon} \to 0 , the EIG1 recovers all but a vanishing part of the underlying permutation \Pi.
Edit intent: clarity
Original:  When \sigma N^{7/6-\epsilon} \to \infty, this algorithm cannot recover more than o(N) correct matches.
Revised:  When \sigma N^{7/6-\epsilon} \to \infty, this method cannot recover more than o(N) correct matches.
Edit intent: clarity
Original: For model-free reinforcement learning,  the main difficulty of stochastic Bellman residual minimization is the double sampling problem, i.e., while only one single sample for the next state is available in the model-free setting, two independent samples for the next state are required in order to perform unbiased stochastic gradient descent.
Revised: For model-free reinforcement learning, one of the main difficulty of stochastic Bellman residual minimization is the double sampling problem, i.e., while only one single sample for the next state is available in the model-free setting, two independent samples for the next state are required in order to perform unbiased stochastic gradient descent.
Edit intent: clarity
Original:  We propose new algorithms for addressing this problem based on the key idea of borrowing extra randomness from the future.
Revised:  We propose new algorithms for addressing this problem based on the idea of borrowing extra randomness from the future.
Edit intent: clarity
Original:  We apply the new algorithms to policy evaluation in both tabular and neural network settings  to confirm the theoretical findings.
Revised:  Numerical results for policy evaluation in both tabular and neural network settings to confirm the theoretical findings.
Edit intent: clarity
Original:  To solve this type of problems, implicit-explicit (IMEX) Runge-Kutta or multistep methods have been widely used and their performance is understood well in the non-stiff regime (\varepsilon=O(1)) and limiting regime (\varepsilon\rightarrow 0).
Revised:  To solve this type of problems, implicit-explicit (IMEX) multistep methods have been widely used and their performance is understood well in the non-stiff regime (\varepsilon=O(1)) and limiting regime (\varepsilon\rightarrow 0).
Edit intent: coherence
Original:  However, in the intermediate regime (say, \varepsilon=O(\Delta t)), some uniform accuracy or order reduction phenomena have been reported numerically without much theoretical justification .
Revised:  However, in the intermediate regime (say, \varepsilon=O(\Delta t)), uniform accuracy has been reported numerically without much theoretical justification .
Edit intent: clarity
Original:  In this work, we prove the uniform accuracy ( an optimal {\it a priori} error bound ) of a class of IMEX multistep methods -- IMEX backward differentiation formulas (IMEX-BDF)  for linear hyperbolic systems with stiff relaxation.
Revised:  In this work, we prove the uniform accuracy -- an optimal {\it a priori} error bound ) of a class of IMEX multistep methods -- IMEX backward differentiation formulas (IMEX-BDF) for linear hyperbolic systems with stiff relaxation.
Edit intent: fluency
Original:  In this work, we prove the uniform accuracy ( an optimal {\it a priori} error bound ) of a class of IMEX multistep methods -- IMEX backward differentiation formulas (IMEX-BDF)  for linear hyperbolic systems with stiff relaxation.
Revised:  In this work, we prove the uniform accuracy ( an optimal {\it a priori} error bound -- of a class of IMEX multistep methods -- IMEX backward differentiation formulas (IMEX-BDF) for linear hyperbolic systems with stiff relaxation.
Edit intent: fluency
Original:  In this work, we prove the uniform accuracy ( an optimal {\it a priori} error bound ) of a class of IMEX multistep methods -- IMEX backward differentiation formulas (IMEX-BDF)  for linear hyperbolic systems with stiff relaxation.
Revised:  In this work, we prove the uniform accuracy ( an optimal {\it a priori} error bound ) of a class of IMEX multistep methods , IMEX backward differentiation formulas (IMEX-BDF) for linear hyperbolic systems with stiff relaxation.
Edit intent: fluency
Original:  In this work, we prove the uniform accuracy ( an optimal {\it a priori} error bound ) of a class of IMEX multistep methods -- IMEX backward differentiation formulas (IMEX-BDF)  for linear hyperbolic systems with stiff relaxation.
Revised:  In this work, we prove the uniform accuracy ( an optimal {\it a priori} error bound ) of a class of IMEX multistep methods -- IMEX backward differentiation formulas (IMEX-BDF) , for linear hyperbolic systems with stiff relaxation.
Edit intent: fluency
Original: This paper outlines BenchCounci 's view on the challenges, rules, and vision of benchmarking modern workloads like Big Data, AI or machine learning, and Internet Services.
Revised: This paper outlines BenchCouncil 's view on the challenges, rules, and vision of benchmarking modern workloads like Big Data, AI or machine learning, and Internet Services.
Edit intent: fluency
Original:  Extending this theorem , Webb (2004) introduced the notion of Pfaffian pairs as a pair of totally unimodular matrices for which counting of their common bases is tractable  .
Revised:  Extending this theorem , Webb (2004) introduced the notion of Pfaffian pairs as a pair of matrices for which counting of their common bases is tractable .
Edit intent: clarity
Original:  Our algorithm makes use of Frank's weight splitting lemma on the weighted matroid intersection .
Revised:  Our algorithm makes use of Frank's weight splitting lemma for the weighted matroid intersection .
Edit intent: fluency
Original:   It enables us to perform diagram chasing as essentially one-way computations led by  rewriting rules.
Revised:  It enables us to perform diagram chasing as essentially one-way computations led by the rewriting rules.
Edit intent: fluency
Original:  The scheme is a first proven positivity-preserving energy stable fully-discretized scheme using standard finite difference discretizations .
Revised:  The scheme is a first proven positivity-preserving and energy stable properties using only standard finite difference discretizations .
Edit intent: clarity
Original:  The scheme is a first proven positivity-preserving energy stable fully-discretized scheme using standard finite difference discretizations .
Revised:  The scheme is a first proven positivity-preserving energy stable fully-discretized scheme using standard finite difference discretization .
Edit intent: fluency
Original:  The difficulty in proving the positivity-preserving property is because the equation is of fourth order in space and maximum principle fails to hold .
Revised:  The difficulty in proving the positivity-preserving property lies in the lack of a maximum principle for fourth order PDEs .
Edit intent: clarity
Original:  To overcome this difficulty, we reformulate the scheme as an optimization problem using the variational structure and use the singularity of the energy functional at zero to prove positivenesss of the numerical scheme.
Revised:  To overcome this difficulty, we reformulate the scheme as an optimization problem based on variational structure and use the singularity of the energy functional at zero to prove positivenesss of the numerical scheme.
Edit intent: clarity
Original:  To overcome this difficulty, we reformulate the scheme as an optimization problem using the variational structure and use the singularity of the energy functional at zero to prove positivenesss of the numerical scheme.
Revised:  To overcome this difficulty, we reformulate the scheme as an optimization problem using the variational structure and use the singular nature of the energy functional at zero to prove positivenesss of the numerical scheme.
Edit intent: clarity
Original: A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamic problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the control function method, whose aim is to obtain homogeneous basis functions for the reduced basis space and the penalty method where the boundary conditions are enforced in the reduced order model using a penalty factor.
Revised: A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamics problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the control function method, whose aim is to obtain homogeneous basis functions for the reduced basis space and the penalty method where the boundary conditions are enforced in the reduced order model using a penalty factor.
Edit intent: fluency
Original: A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamic problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the control function method, whose aim is to obtain homogeneous basis functions for the reduced basis space and the penalty method where the boundary conditions are enforced in the reduced order model using a penalty factor.
Revised: A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamic problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the lifting function method, whose aim is to obtain homogeneous basis functions for the reduced basis space and the penalty method where the boundary conditions are enforced in the reduced order model using a penalty factor.
Edit intent: fluency
Original:  Finally, the speedup ratio between the reduced order models and the full order model is of the order 1000 for the lid driven cavity case and of the order 100 for the Y-junction test case.
Revised:  Finally, the reduced order models and the full order model is of the order 1000 for the lid driven cavity case and of the order 100 for the Y-junction test case.
Edit intent: clarity
Original:  Finally, the speedup ratio between the reduced order models and the full order model is of the order 1000 for the lid driven cavity case and of the order 100 for the Y-junction test case.
Revised:  Finally, the speedup ratio between the reduced order models and the full order models for the lid driven cavity case and of the order 100 for the Y-junction test case.
Edit intent: clarity