wanyu/IteraTeR_v2 huggingface dataset:
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 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 .
Revised:  We consider both the access and core parts of the network, and formulate a novel optimization problem which performs the power and spectrum allocation in radio, and service function chaining and scheduling in the NFV environment while guaranteeing the distinct QoS constraints of the requested services .
Edit intent: clarity
Original:  An additional feature of the proposed solution technique is that solving a problem where an interface or layer property is changed require an update in the precomputation that cost linearly with respect to the number points on the affected interfaces with a small constant prefactor .
Revised:  An additional feature of the proposed solution technique is that solving a problem where an interface or layer property is changed , the direct solver can be updated for a cost that scales linearly with respect to the number points on the affected interfaces with a small constant prefactor .
Edit intent: clarity
Original:  The computational cost of the solver scales linearly with respect to the number of discretization points on the interfaces and is able to reuse the bulk of the precomputation cost for any choice of incident wave.
Revised:  The computational cost of the solver scales linearly with respect to the number of discretization points on the interfaces and is able to reuse the bulk of the precomputation can be re-used for any choice of incident wave.
Edit intent: clarity
Original:  When the interface geometries are complex, the dominate term in computational cost of creating the direct solver scales O(NI) where N is the number  discretization points on an interface and I is the number of interfaces.
Revised:  When the interface geometries are complex, the dominant term in the computational cost of creating the direct solver scales O(NI) where N is the number discretization points on an interface and I is the number of interfaces.
Edit intent: fluency
Original:  When the interface geometries are complex, the dominate term in computational cost of creating the direct solver scales O(NI) where N is the number  discretization points on an interface and I is the number of interfaces.
Revised:  When the interface geometries are complex, the dominate term in computational cost of creating the direct solver scales O(NI) where N is the number of discretization points on an interface and I is the number of interfaces.
Edit intent: fluency
Original:  When the interface geometries are complex, the dominate term in computational cost of creating the direct solver scales O(NI) where N is the number  discretization points on an interface and I is the number of interfaces.
Revised:  When the interface geometries are complex, the dominate term in computational cost of creating the direct solver scales O(NI) where N is the number discretization points on each interface and I is the number of interfaces.
Edit intent: clarity
Original:  An added benefit of the presented solver is that building an updated the solver for a new geometry involving a replaced interface or  change in material property in a layer is inexpensive compared to building a new fast direct solver from scratch.
Revised:  An added benefit of the presented solver is that building an updated solver for a new geometry involving a replaced interface or change in material property in a layer is inexpensive compared to building a new fast direct solver from scratch.
Edit intent: fluency
Original:  An added benefit of the presented solver is that building an updated the solver for a new geometry involving a replaced interface or  change in material property in a layer is inexpensive compared to building a new fast direct solver from scratch.
Revised:  An added benefit of the presented solver is that building an updated the solver for a new geometry involving a replaced interface or a change in material property in a layer is inexpensive compared to building a new fast direct solver from scratch.
Edit intent: fluency
Original:  An added benefit of the presented solver is that building an updated the solver for a new geometry involving a replaced interface or  change in material property in a layer is inexpensive compared to building a new fast direct solver from scratch.
Revised:  An added benefit of the presented solver is that building an updated the solver for a new geometry involving a replaced interface or change in material property in one layer is inexpensive compared to building a new fast direct solver from scratch.
Edit intent: clarity
Original: We study the multi-level order-flow imbalance (MLOFI) , which measures the net flow of buy and sell orders at different price levels in a limit order book (LOB).
Revised: We study the , which measures the net flow of buy and sell orders at different price levels in a limit order book (LOB).
Edit intent: clarity
Original:  Using a recent, high-quality data set for 6 liquid stocks on Nasdaq, we use Ridge regression to fit a simple, linear relationship between MLOFI and the contemporaneous change in mid-price.
Revised:  Using a recent, high-quality data set for 6 liquid stocks on Nasdaq, we fit a simple, linear relationship between MLOFI and the contemporaneous change in mid-price.
Edit intent: clarity
Original:  Our results underline how the complex order-flow activity deep into the LOB can influence the price-formation process.
Revised:  Our results underline how order-flow activity deep into the LOB can influence the price-formation process.
Edit intent: clarity
Original:  The present framework provides a new bold and promising direction towards the development of a unified theory of decisions in the presence of uncertainty.
Revised:  The present framework provides a promising direction towards the development of a unified theory of decisions in the presence of uncertainty.
Edit intent: clarity
Original: Candidate retrieval is a crucial part in recommendation system , where quality candidates need to be selected in realtime for user's recommendation request.
Revised: Candidate retrieval is a fundamental issue in recommendation system , where quality candidates need to be selected in realtime for user's recommendation request.
Edit intent: clarity
Original: Candidate retrieval is a crucial part in recommendation system , where quality candidates need to be selected in realtime for user's recommendation request.
Revised: Candidate retrieval is a crucial part in recommendation system . Given user's recommendation request, relevant candidates need to be selected in realtime for user's recommendation request.
Edit intent: clarity
Original: Candidate retrieval is a crucial part in recommendation system , where quality candidates need to be selected in realtime for user's recommendation request.
Revised: Candidate retrieval is a crucial part in recommendation system , where quality candidates need to be retrieved in realtime for user's recommendation request.
Edit intent: clarity
Original:  In contrast,  deep learning-based recommenders are precise in modeling user interest, but they are difficult to be scaled for efficient candidate retrieval .
Revised:  In contrast, those deep learning-based recommenders are precise in modeling user interest, but they are difficult to be scaled for efficient candidate retrieval .
Edit intent: clarity
Original:  In contrast,  deep learning-based recommenders are precise in modeling user interest, but they are difficult to be scaled for efficient candidate retrieval .
Revised:  In contrast, deep learning-based approaches can be highly accurate in identifying relevant items; yet, they are unsuitable for candidate retrieval due to their inherent limitation on scalability .
Edit intent: clarity
Original:  We propose that recommendation systems (RSs) should take into account the expected QoS with which a content can be delivered to a user , to increase the user satisfaction and retention rates.
Revised:  We propose that recommendation systems (RSs) should take into account the expected QoS with which a content can be delivered , to increase the user satisfaction and retention rates.
Edit intent: clarity
Original:  While QoS-aware (or, network-aware) recommendations have been  recently proposed as a promising solution to improve network performance , the impact of this idea on real user experience has only been speculated.
Revised:  While QoS-aware (or, network-aware) recommendations have been very recently proposed as a promising solution to improve network performance , the impact of this idea on real user experience has only been speculated.
Edit intent: coherence
Original:  Our analysis demonstrates the potential of the idea: QoS-aware recommendations could be beneficial for both the users (better experience) and content providers (higher retention rates).
Revised:  Our analysis demonstrates the potential of the idea: QoS-aware RSs could be beneficial for both the users (better experience) and content providers (higher retention rates).
Edit intent: clarity
Original: Optimal control problems including partial differential equation (PDE) as well as integer constraints combine the combinatorial difficulties of integer programming and  large-scale systems resulting from discretizing the PDE.
Revised: Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and large-scale systems resulting from discretizing the PDE.
Edit intent: fluency
Original: Optimal control problems including partial differential equation (PDE) as well as integer constraints combine the combinatorial difficulties of integer programming and  large-scale systems resulting from discretizing the PDE.
Revised: Optimal control problems including partial differential equation (PDE) as well as integer constraints combine the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretizing the PDE.
Edit intent: clarity
Original:  A common solution strategy for such a problem would be Branch-and-Bound .
Revised:  A common solution strategy for such problems .
Edit intent: coherence
Original: We present a new algorithm for finding compact neural networks encoding reinforcement learning (RL) policies .
Revised: We present a neural architecture search algorithm to construct compact reinforcement learning (RL) policies .
Edit intent: clarity
Original:  To do it, we leverage in the novel RL setting the theory of pointer networks and ENAS-type algorithms for combinatorial optimization of RL policies as well as recent evolution strategies (ES ) optimization methods, and propose to define the combinatorial search space  to be the the set of different edge-partitionings (colorings) into same-weight classes  .
Revised:  To do it, we leverage in the novel RL setting the theory of pointer networks and ENAS-type algorithms for combinatorial optimization of RL policies as well as recent evolution strategies (ES ) optimization methods, and propose to define the combinatorial search space of NAS to be the the set of different edge-partitionings (colorings) into same-weight classes .
Edit intent: clarity
Original:  To do it, we leverage in the novel RL setting the theory of pointer networks and ENAS-type algorithms for combinatorial optimization of RL policies as well as recent evolution strategies (ES ) optimization methods, and propose to define the combinatorial search space  to be the the set of different edge-partitionings (colorings) into same-weight classes  .
Revised:  To do it, we leverage in the novel RL setting the theory of pointer networks and ENAS-type algorithms for combinatorial optimization of RL policies as well as recent evolution strategies (ES ) optimization methods, and propose to define the combinatorial search space to be the set of different edge-partitionings (colorings) into same-weight classes .
Edit intent: fluency
Original:  Given a graph G and an integer budget k, we seek to find a connected subset of at most k vertices which maximizes the number of dominated vertices in G. We answer an open question in [Khuller, Purohit, and Sarpatwar,\ SODA 2014] and thus we improve over the previous (1-1/e)/13 approximation.
Revised:  Given a graph G and an integer budget k, we seek to find a connected subset of at most k vertices which maximizes the number of dominated vertices in G. We improve over the previous (1-1/e)/13 approximation in [Khuller, Purohit, and Sarpatwar,\ SODA 2014] and thus we improve over the previous (1-1/e)/13 approximation.
Edit intent: clarity
Original:  We notice that, in the connected case, BEVD becomes equivalent to BCDS. Moreover, we examine the ``dual'' \emph{partial edge-vertex domination} (PEVD) problem, where a graph G and a quota n' are given.
Revised:  We notice that, in the connected case, BEVD becomes equivalent to BCDS. Moreover, we examine the "dual" \emph{partial edge-vertex domination} (PEVD) problem, where a graph G and a quota n' are given.
Edit intent: fluency
Original:  The main result of this paper is a degree type result, which generalizes Brooks' theorem, Gallai's theorem, degree-choosable  , signed degree-colorable , DP-degree-colorable  . Similar to Borodin, Kostochka and Toft's variable degeneracy, the degree type result is also self-strengthening.
Revised:  The main result of this paper is a degree type result, which generalizes Brooks' theorem, Gallai's theorem, degree-choosable result , signed degree-colorable , DP-degree-colorable . Similar to Borodin, Kostochka and Toft's variable degeneracy, the degree type result is also self-strengthening.
Edit intent: fluency
Original:  The main result of this paper is a degree type result, which generalizes Brooks' theorem, Gallai's theorem, degree-choosable  , signed degree-colorable , DP-degree-colorable  . Similar to Borodin, Kostochka and Toft's variable degeneracy, the degree type result is also self-strengthening.
Revised:  The main result of this paper is a degree type result, which generalizes Brooks' theorem, Gallai's theorem, degree-choosable , signed degree-colorable result, and DP-degree-colorable . Similar to Borodin, Kostochka and Toft's variable degeneracy, the degree type result is also self-strengthening.
Edit intent: coherence
Original:  The main result of this paper is a degree type result, which generalizes Brooks' theorem, Gallai's theorem, degree-choosable  , signed degree-colorable , DP-degree-colorable  . Similar to Borodin, Kostochka and Toft's variable degeneracy, the degree type result is also self-strengthening.
Revised:  The main result of this paper is a degree type result, which generalizes Brooks' theorem, Gallai's theorem, degree-choosable , signed degree-colorable , DP-degree-colorable result . Similar to Borodin, Kostochka and Toft's variable degeneracy, the degree type result is also self-strengthening.
Edit intent: fluency
Original:  The main result of this paper is a degree type result, which generalizes Brooks' theorem, Gallai's theorem, degree-choosable  , signed degree-colorable , DP-degree-colorable  . Similar to Borodin, Kostochka and Toft's variable degeneracy, the degree type result is also self-strengthening.
Revised:  The main result of this paper is a degree type result, which generalizes Brooks' theorem, Gallai's theorem, degree-choosable , signed degree-colorable , DP-degree-colorable . Similar to Borodin, Kostochka and Toft's variable degeneracy, this degree type result is also self-strengthening.
Edit intent: fluency
Original: Let f be a nonnegative integer valued function on the vertex-set of a graph.
Revised: Let f be a nonnegative integer valued function on the vertex set of a graph.
Edit intent: fluency
Original:  In this paper, we define a new concept, strictly f-degenerate transversal, which generalizes list coloring,  (f_{1}, f_{2}, \dots, f_{ \kappa })-partition , signed coloring, DP-coloring and L-forested-coloring .
Revised:  In this paper, we define a new concept, strictly f-degenerate transversal, which generalizes list coloring, signed coloring, DP-coloring, L-forested-coloring, and (f_{1}, f_{2}, \dots, f_{ \kappa })-partition , signed coloring, DP-coloring and L-forested-coloring .
Edit intent: coherence
Original:  In this paper, we define a new concept, strictly f-degenerate transversal, which generalizes list coloring,  (f_{1}, f_{2}, \dots, f_{ \kappa })-partition , signed coloring, DP-coloring and L-forested-coloring .
Revised:  In this paper, we define a new concept, strictly f-degenerate transversal, which generalizes list coloring, (f_{1}, f_{2}, \dots, f_{ \kappa })-partition .
Edit intent: coherence
Original:  A {\bf cover} of a graph G is a graph H with vertex set V(H) = v \in V(G) X_{v}, where X_{v} = \{(v, 1), (v, 2), \dots, (v, \kappa )\};
Revised:  A {\bf cover} of a graph G is a graph H with vertex set V(H) = v \in V(G) X_{v}, where X_{v} = \{(v, 1), (v, 2), \dots, (v, s )\};
Edit intent: clarity
Original:  In the final section, we give some open problems.
Revised:  In the final section, we pose some open problems.
Edit intent: clarity
Original:  \ for the treatment of order/disorder transitions of molecular systems can be successfully employed to analyze the transitions and help design alchemical schedules and soft-core functions that avoid or reduce the adverse effects of rare binding/unbinding transitions.
Revised:  for the treatment of order/disorder transitions of molecular systems can be successfully employed to analyze the transitions and help design alchemical schedules and soft-core functions that avoid or reduce the adverse effects of rare binding/unbinding transitions.
Edit intent: clarity
Original:  In this paper, we break through this barrier and present Quant GANs, a data-driven model which is inspired by the recent success of generative adversarial networks (GANs).
Revised:  As an alternative, we introduce Quant GANs, a data-driven model which is inspired by the recent success of generative adversarial networks (GANs).
Edit intent: clarity
Original:  Furthermore, the generator function is explicitly constructed such that the induced stochastic process allows a transition to its risk-neutral distribution.
Revised:  The generator function is explicitly constructed such that the induced stochastic process allows a transition to its risk-neutral distribution.
Edit intent: coherence
Original:  However, the tree-depth of a constraint matrix depends on the positions of its non-zero entries and thus does not reflect its geometric nature , in particular, is not invariant under row operations.
Revised:  However, the tree-depth of a constraint matrix depends on the positions of its non-zero entries and thus does not reflect its geometric structure , in particular, is not invariant under row operations.
Edit intent: clarity
Original: A long line of research on fixed parameter tractability of integer programming culminated with showing that integer programs with n variables and a constraint matrix with  tree-depth d and largest entry D are solvable in in time g(d,D)poly(n) for some function g , i. e., fixed parameter tractable when parameterized by tree-depth d and D.
Revised: A long line of research on fixed parameter tractability of integer programming culminated with showing that integer programs with n variables and a constraint matrix with tree-depth d and largest entry D are solvable in time g(d,D)poly(n) for some function g , i. e., fixed parameter tractable when parameterized by tree-depth d and D.
Edit intent: fluency
Original: A long line of research on fixed parameter tractability of integer programming culminated with showing that integer programs with n variables and a constraint matrix with  tree-depth d and largest entry D are solvable in in time g(d,D)poly(n) for some function g , i. e., fixed parameter tractable when parameterized by tree-depth d and D.
Revised: A long line of research on fixed parameter tractability of integer programming culminated with showing that integer programs with n variables and a constraint matrix with tree-depth d and largest entry D are solvable in in time g(d,D)poly(n) for some function g .
Edit intent: coherence
Original:  However, the  tree-depth of a constraint matrix depends on the positions of its non-zero entries and thus does not reflect its geometric structure , in particular, is not invariant under row operations .
Revised:  However, the tree-depth of a constraint matrix depends on the positions of its non-zero entries and thus does not reflect its geometric structure .
Edit intent: coherence
Original:  We prove that the  branch-depth of the matroid defined by the columns of the constraint matrixis equal to the minimum tree-depth of a row-equivalent matrix, and we strengthen the fixed parameter algorithm for integer programs with bounded tree-depth by showing that integer programs whose matrix has branch-depth d and largest entry D are solvable in time h(d ,D)poly(n) . The parameterization by branch-depth cannot be replaced by the more permissive notion of branch-width.
Revised:  We prove that the branch-depth of the matroid defined by the columns of the matrix. We design a fixed parameter algorithm for computing branch-depth of matroids represented over a finite field and a row-equivalent matrix, and we strengthen the fixed parameter algorithm for integer programs with bounded tree-depth by showing that integer programs whose matrix has branch-depth d and largest entry D are solvable in time h(d ,D)poly(n) . The parameterization by branch-depth cannot be replaced by the more permissive notion of branch-width.
Edit intent: clarity
Original:  We prove that the  branch-depth of the matroid defined by the columns of the constraint matrixis equal to the minimum tree-depth of a row-equivalent matrix, and we strengthen the fixed parameter algorithm for integer programs with bounded tree-depth by showing that integer programs whose matrix has branch-depth d and largest entry D are solvable in time h(d ,D)poly(n) . The parameterization by branch-depth cannot be replaced by the more permissive notion of branch-width.
Revised:  We prove that the branch-depth of the matroid defined by the columns of the constraint matrixis equal to the minimum tree-depth of a fixed parameter algorithm for integer programs with bounded tree-depth by showing that integer programs whose matrix has branch-depth d and largest entry D are solvable in time h(d ,D)poly(n) . The parameterization by branch-depth cannot be replaced by the more permissive notion of branch-width.
Edit intent: coherence
Original:  We prove that the  branch-depth of the matroid defined by the columns of the constraint matrixis equal to the minimum tree-depth of a row-equivalent matrix, and we strengthen the fixed parameter algorithm for integer programs with bounded tree-depth by showing that integer programs whose matrix has branch-depth d and largest entry D are solvable in time h(d ,D)poly(n) . The parameterization by branch-depth cannot be replaced by the more permissive notion of branch-width.
Revised:  We prove that the branch-depth of the matroid defined by the columns of the constraint matrixis equal to the minimum tree-depth of a row-equivalent matrix, and we strengthen the fixed parameter algorithm for computing a row-equivalent matrix with minimum dual tree-depth by showing that integer programs whose matrix has branch-depth d and largest entry D are solvable in time h(d ,D)poly(n) . The parameterization by branch-depth cannot be replaced by the more permissive notion of branch-width.
Edit intent: clarity