wanyu/IteraTeR_v2 huggingface dataset:
Original:  A 2-stage stochastic IP is an integer program of the form \max \{ c^T x \mid Ax = b, l \leq x \leq u, x \in Z ^n \} where the constraint matrix A \in Z^{ s \times r  } consists roughly of n repetition of a block matrix A on the vertical line and n repetitions of a matrix B \in Z^{ t \times r  } on the diagonal.
Revised:  A 2-stage stochastic IP is an integer program of the form \max \{ c^T x \mid Ax = b, l \leq x \leq u, x \in Z ^n \} where the constraint matrix A \in Z^{ r } consists roughly of n repetition of a block matrix A on the vertical line and n repetitions of a matrix B \in Z^{ t \times r } on the diagonal.
Edit intent: clarity
Original:  A 2-stage stochastic IP is an integer program of the form \max \{ c^T x \mid Ax = b, l \leq x \leq u, x \in Z ^n \} where the constraint matrix A \in Z^{ s \times r  } consists roughly of n repetition of a block matrix A on the vertical line and n repetitions of a matrix B \in Z^{ t \times r  } on the diagonal.
Revised:  A 2-stage stochastic IP is an integer program of the form \max \{ c^T x \mid Ax = b, l \leq x \leq u, x \in Z ^n \} where the constraint matrix A \in Z^{ s \times r } consists roughly of n repetition of a block matrix A on the vertical line and n repetitions of a matrix B \in Z^{ r } on the diagonal.
Edit intent: fluency
Original:  The algorithm is based on the Graver augmentation framework where our main contribution is to give an explicit double exponential bound on the size of the augmenting steps.
Revised:  The algorithm is based on the Graver augmentation framework where our main contribution is to give an explicit doubly exponential bound on the size of the augmenting steps.
Edit intent: fluency
Original:  The previous bound for the size of the augmenting steps relied on non-constructive finiteness arguments from computational algebra and therefore only am implicit bound was known that depends on parameters r,s,t and \Delta, where \Delta is the largest entry od the constraint matrix.
Revised:  The previous bound for the size of the augmenting steps relied on non-constructive finiteness arguments from commutative algebra and therefore only am implicit bound was known that depends on parameters r,s,t and \Delta, where \Delta is the largest entry od the constraint matrix.
Edit intent: clarity
Original:  The previous bound for the size of the augmenting steps relied on non-constructive finiteness arguments from computational algebra and therefore only am implicit bound was known that depends on parameters r,s,t and \Delta, where \Delta is the largest entry od the constraint matrix.
Revised:  The previous bound for the size of the augmenting steps relied on non-constructive finiteness arguments from computational algebra and therefore only an implicit bound was known that depends on parameters r,s,t and \Delta, where \Delta is the largest entry od the constraint matrix.
Edit intent: fluency
Original:  The previous bound for the size of the augmenting steps relied on non-constructive finiteness arguments from computational algebra and therefore only am implicit bound was known that depends on parameters r,s,t and \Delta, where \Delta is the largest entry od the constraint matrix.
Revised:  The previous bound for the size of the augmenting steps relied on non-constructive finiteness arguments from computational algebra and therefore only am implicit bound was known that depends on parameters r,s,t and \Delta, where \Delta is the largest entry of the constraint matrix.
Edit intent: fluency
Original:  As a result of our new bound we obtain an algorithm to solve 2-stage stochastic IPs in time poly(n,t) \cdot f(r,s,\Delta), where f is a double exponential function.
Revised:  As a result of our new bound we obtain an algorithm to solve 2-stage stochastic IPs in time poly(n,t) \cdot f(r,s,\Delta), where f is a doubly exponential function.
Edit intent: clarity
Original:  To complement our result, we also prove a double exponential lower bound for the size of the augmenting steps.
Revised:  To complement our result, we also prove a doubly exponential lower bound for the size of the augmenting steps.
Edit intent: fluency
Original:  Both lower bounds hold when n=\Omega(k) . The lower bound for Disjointness improves over the lower bound that can be inferred from the result of Braverman et al.  (FOCS 2013), which was proved in the coordinator model and can yield a lower bound of \Omega(kn/\log k) in the peer-to-peer model.
Revised:  Both lower bounds hold when n=\Omega(k) . The lower bound for Disjointness improves over the lower bound that can be inferred from the result of Braverman et al. ~ (FOCS 2013), which was proved in the coordinator model and can yield a lower bound of \Omega(kn/\log k) in the peer-to-peer model.
Edit intent: fluency
Original:  The expanded form of the linear problem is not solved directlybut it is exploited instead to extract all eigenvalues in a certain region of the complex plane .
Revised:  The expanded form of this linearization are not extracted directly. Instead, its structure is exploited to develop a scheme that allows to extract all eigenvalues in a certain region of the complex plane .
Edit intent: clarity
Original:  A few theoretical results are established to explain why the  approach works and a few numerical experiments are described to validate it .
Revised:  A few theoretical results are established to explain why the approach works and numerical experiments are described to validate it .
Edit intent: fluency
Original:  A few theoretical results are established to explain why the  approach works and a few numerical experiments are described to validate it .
Revised:  A few theoretical results are established to explain why the approach works and a few numerical experiments are presented to validate the proposed algorithm .
Edit intent: clarity
Original: We introduce and asses a Divide \& Conquer heuristic method, aimed to solve large instances of the  Knapsack Problem.
Revised: We introduce and asses a Divide \& Conquer heuristic strategies aimed to solve large instances of the Knapsack Problem.
Edit intent: clarity
Original: We propose a new model of the oculomotor system, particularly the vestibulo-ocular reflex, the optokinetic reflex, gaze fixation, and smooth pursuit.
Revised: We propose a new model of the oculomotor system, particularly the vestibulo-ocular reflex, gaze fixation, and smooth pursuit.
Edit intent: clarity
Original: We investigate the time-complexity of the All-Pairs Max-Flow problem: Given a graph with n nodes and m edges, compute for all pairs of nodes the maximum-flow value between them.
Revised: We investigate the time-complexity of the All-Pairs Max-Flow problem: Given a graph with n nodes and m edges, compute for all pairs of nodes the maximum-flow value between them.
Edit intent: fluency
Original:  If Max-Flow (the version with a given source-sink pair s,t) can be solved in time T(m), then an O(n^2) \cdot T(m) is a trivial upper bound.
Revised:  If Max-Flow (the version with a given source-sink pair s,t) can be solved in time T(m), then an O(n^2) \cdot T(m) is a trivial upper bound.
Edit intent: fluency
Original:  Under the plausible assumption that Max-Flow can be solved in near-linear time m^{1+o(1)}, this half-century old algorithm yields an nm^{1+o(1)} bound.
Revised:  Under the plausible assumption that Max-Flow can be solved in near-linear time m^{1+o(1)}, this half-century old algorithm yields an nm^{1+o(1)} bound.
Edit intent: fluency
Original:  We design the first hardness reductions for All-Pairs Max-Flow in undirected graphs, giving an essentially optimal lower bound for the node-capacities setting.
Revised:  We design the first hardness reductions for All-Pairs Max-Flow in undirected graphs, giving an essentially optimal lower bound for the node-capacities setting.
Edit intent: fluency
Original:  Even with current Max-Flow algorithms we improve state-of-the-art in many density regimes.
Revised:  Even with current Max-Flow algorithms we improve state-of-the-art in many density regimes.
Edit intent: fluency
Original: Using precise times of every spike, spiking supervised learning has more effects on complex spatial-temporal pattern than that only through neuronal firing rates.
Revised: Using precise times of every spike, spiking supervised learning has more effects on complex spatial-temporal pattern than supervised learning only through neuronal firing rates.
Edit intent: clarity
Original:  The purpose of spiking supervised learning after temporal encoding is to make neural networks emit desired spike trains with precise firing time . Existing algorithms of spiking supervised learning have excellent performances, but mechanisms of them are most in an offline pattern or still have some problems  . Based on an online regulative mechanism of biological neuronal synapses, this paper proposes an online supervised learning algorithm of multiple spike trains for spiking neural networks.
Revised:  The purpose of spiking supervised learning after temporal encoding is to emit desired spike trains with precise firing time . Existing algorithms of spiking supervised learning have excellent performances, but mechanisms of them are most in an offline pattern or still have some problems . Based on an online regulative mechanism of biological neuronal synapses, this paper proposes an online supervised learning algorithm of multiple spike trains for spiking neural networks.
Edit intent: clarity
Original:  The purpose of spiking supervised learning after temporal encoding is to make neural networks emit desired spike trains with precise firing time . Existing algorithms of spiking supervised learning have excellent performances, but mechanisms of them are most in an offline pattern or still have some problems  . Based on an online regulative mechanism of biological neuronal synapses, this paper proposes an online supervised learning algorithm of multiple spike trains for spiking neural networks.
Revised:  The purpose of spiking supervised learning after temporal encoding is to make neural networks emit desired spike trains with precise times . Existing algorithms of spiking supervised learning have excellent performances, but mechanisms of them are most in an offline pattern or still have some problems . Based on an online regulative mechanism of biological neuronal synapses, this paper proposes an online supervised learning algorithm of multiple spike trains for spiking neural networks.
Edit intent: clarity
Original:  The purpose of spiking supervised learning after temporal encoding is to make neural networks emit desired spike trains with precise firing time . Existing algorithms of spiking supervised learning have excellent performances, but mechanisms of them are most in an offline pattern or still have some problems  . Based on an online regulative mechanism of biological neuronal synapses, this paper proposes an online supervised learning algorithm of multiple spike trains for spiking neural networks.
Revised:  The purpose of spiking supervised learning after temporal encoding is to make neural networks emit desired spike trains with precise firing time . Existing algorithms of spiking supervised learning have excellent performances, but mechanisms of them still have some problems . Based on an online regulative mechanism of biological neuronal synapses, this paper proposes an online supervised learning algorithm of multiple spike trains for spiking neural networks.
Edit intent: coherence
Original:  The purpose of spiking supervised learning after temporal encoding is to make neural networks emit desired spike trains with precise firing time . Existing algorithms of spiking supervised learning have excellent performances, but mechanisms of them are most in an offline pattern or still have some problems  . Based on an online regulative mechanism of biological neuronal synapses, this paper proposes an online supervised learning algorithm of multiple spike trains for spiking neural networks.
Revised:  The purpose of spiking supervised learning after temporal encoding is to make neural networks emit desired spike trains with precise firing time . Existing algorithms of spiking supervised learning have excellent performances, but mechanisms of them are most in an offline pattern or still have some problems . Based on an online regulative mechanism of biological synapses, this paper proposes an online supervised learning algorithm of multiple spike trains for spiking neural networks.
Edit intent: clarity
Original:   Relationship among desired output, actual output and input spike trains is firstly analyzed and synthesized to select spikes simply and correctly for a direct regulation , and then a computational method is constructed based on simple triple spikes using this direct regulation.
Revised:  Relationship among desired output, actual output and input spike trains is firstly analyzed and synthesized to select spikes simply and correctly for a direct regulation . And then a computational method is constructed based on simple triple spikes using this direct regulation.
Edit intent: coherence
Original:  Results of experiments show that this online supervised algorithm improves learning performance obviously compared with offline pattern and has higher learning accuracy and efficiency than other learning algorithms .
Revised:  Compared with other learning algorithms, results of experiments show that this online supervised algorithm improves learning performance obviously compared with offline pattern and has higher learning accuracy and efficiency than other learning algorithms .
Edit intent: clarity
Original:  Results of experiments show that this online supervised algorithm improves learning performance obviously compared with offline pattern and has higher learning accuracy and efficiency than other learning algorithms .
Revised:  Results of experiments show that proposed algorithm has higher learning accuracy and efficiency than other learning algorithms .
Edit intent: clarity
Original:  Results of experiments show that this online supervised algorithm improves learning performance obviously compared with offline pattern and has higher learning accuracy and efficiency than other learning algorithms .
Revised:  Results of experiments show that this online supervised algorithm improves learning performance obviously compared with offline pattern and has higher learning accuracy and efficiency .
Edit intent: clarity
Original:  In this paper, we consider a p-multigrid method, in which each level of the hierarchy is associated with a different approximation order p instead of  mesh width h. Since the use of classical smoothers ( i.e. Gauss-Seidel) results in a p-multigrid method with deteriorating performance for higher values of p, the use of an ILUT smoother is investigated.
Revised:  In this paper, we consider a p-multigrid method, in which coarsening is applied in the approximation order p instead of mesh width h. Since the use of classical smoothers ( i.e. Gauss-Seidel) results in a p-multigrid method with deteriorating performance for higher values of p, the use of an ILUT smoother is investigated.
Edit intent: clarity
Original:  In this paper, we consider a p-multigrid method, in which each level of the hierarchy is associated with a different approximation order p instead of  mesh width h. Since the use of classical smoothers ( i.e. Gauss-Seidel) results in a p-multigrid method with deteriorating performance for higher values of p, the use of an ILUT smoother is investigated.
Revised:  In this paper, we consider a p-multigrid method, in which each level of the hierarchy is associated with a different approximation order p instead of the mesh width h. Since the use of classical smoothers ( i.e. Gauss-Seidel) results in a p-multigrid method with deteriorating performance for higher values of p, the use of an ILUT smoother is investigated.
Edit intent: fluency
Original:  In this paper, we consider a p-multigrid method, in which each level of the hierarchy is associated with a different approximation order p instead of  mesh width h. Since the use of classical smoothers ( i.e. Gauss-Seidel) results in a p-multigrid method with deteriorating performance for higher values of p, the use of an ILUT smoother is investigated.
Revised:  In this paper, we consider a p-multigrid method, in which each level of the hierarchy is associated with a different approximation order p instead of mesh width h. Since the use of classical smoothers ( e.g. Gauss-Seidel) results in a p-multigrid method with deteriorating performance for higher values of p, the use of an ILUT smoother is investigated.
Edit intent: fluency
Original:  Otherwise, security services could affect  quality of service experienced by customers.
Revised:  Otherwise, security services could affect the quality of service experienced by customers.
Edit intent: fluency
Original:  In this paper , we propose PESS (Progressive Embedding of Security Services), a solution to dynamically provision security services by selecting the most appropriate combination and placement of VSNFs that cater to the needs of each application , while optimizing resource utilization.
Revised:  In this paper we propose PESS (Progressive Embedding of Security Services), a solution to dynamically provision security services by selecting the most appropriate combination and placement of VSNFs that cater to the needs of each application , while optimizing resource utilization.
Edit intent: fluency
Original:  In this paper , we propose PESS (Progressive Embedding of Security Services), a solution to dynamically provision security services by selecting the most appropriate combination and placement of VSNFs that cater to the needs of each application , while optimizing resource utilization.
Revised:  In this paper , we propose PESS (Progressive Embedding of Security Services), a solution to efficiently deploy chains of virtualised security functions based on the security requirements of individual applications and operators' policies , while optimizing resource utilization.
Edit intent: clarity
Original:  We provide  PESS mathematical model and heuristic solution.
Revised:  We provide the PESS mathematical model and heuristic solution.
Edit intent: clarity
Original:  This result ultimately leads to a higher number of provisioned security services and to up to a three-fold reduction in end-to-end latency of application traffic.
Revised:  This result ultimately leads to a higher number of provisioned security services and to up to a threefold reduction in end-to-end latency of application traffic.
Edit intent: fluency
Original: We adopt an interior penalty discontinuous Galerkin method using a patch reconstructed approximate space to solve the elliptic eigenvalue problems, including both the second and fourth order problem in 2D and 3D.
Revised: We adopt an interior penalty discontinuous Galerkin method using a patch reconstructed approximation space to solve the elliptic eigenvalue problems, including both the second and fourth order problem in 2D and 3D.
Edit intent: fluency
Original: We adopt an interior penalty discontinuous Galerkin method using a patch reconstructed approximate space to solve the elliptic eigenvalue problems, including both the second and fourth order problem in 2D and 3D.
Revised: We adopt an interior penalty discontinuous Galerkin method using a patch reconstructed approximate space to solve elliptic eigenvalue problems, including both the second and fourth order problem in 2D and 3D.
Edit intent: fluency
Original: We adopt an interior penalty discontinuous Galerkin method using a patch reconstructed approximate space to solve the elliptic eigenvalue problems, including both the second and fourth order problem in 2D and 3D.
Revised: We adopt an interior penalty discontinuous Galerkin method using a patch reconstructed approximate space to solve the elliptic eigenvalue problems, including both second and fourth order problem in 2D and 3D.
Edit intent: fluency
Original: We adopt an interior penalty discontinuous Galerkin method using a patch reconstructed approximate space to solve the elliptic eigenvalue problems, including both the second and fourth order problem in 2D and 3D.
Revised: We adopt an interior penalty discontinuous Galerkin method using a patch reconstructed approximate space to solve the elliptic eigenvalue problems, including both the second and fourth order problems in 2D and 3D.
Edit intent: fluency
Original:  It is a direct extension of the method recently proposed to solve corresponding boundary value problems, that the optimal error estimates of the approximation to eigenfunctions and eigenvalues are instant consequences from existed results.
Revised:  It is a direct extension of the method recently proposed to solve corresponding boundary value problems, and the optimal error estimates of the approximation to eigenfunctions and eigenvalues are instant consequences from existed results.
Edit intent: coherence
Original:  It is a direct extension of the method recently proposed to solve corresponding boundary value problems, that the optimal error estimates of the approximation to eigenfunctions and eigenvalues are instant consequences from existed results.
Revised:  It is a direct extension of the method recently proposed to solve corresponding boundary value problems, that the optimal error estimates of the approximation to eigenfunctions and eigenvalues are instant consequences from existing results.
Edit intent: fluency
Original:  The method enjoys the advantages that it uses only one degree of freedom on each element to achieve very high order accuracy, which is highly preferred for eigenvalue problems as implied by Zhang's recent study [J. Sci. Comput.
Revised:  The method enjoys the advantage that it uses only one degree of freedom on each element to achieve very high order accuracy, which is highly preferred for eigenvalue problems as implied by Zhang's recent study [J. Sci. Comput.
Edit intent: fluency
Original:  By numerical results, we illustrate that high order methods can provide much more reliable eigenvalues.
Revised:  By numerical results, we illustrate that higher order methods can provide much more reliable eigenvalues.
Edit intent: fluency
Original:  To justify that our method is the right one for eigenvalue problems, we show that the patch reconstructed approximate space attains the same accuracy with much less degree of freedoms than classical discontinuous Galerkin methods.
Revised:  To justify that our method is the right one for eigenvalue problems, we show that the patch reconstructed approximation space attains the same accuracy with much less degree of freedoms than classical discontinuous Galerkin methods.
Edit intent: fluency
Original:  To justify that our method is the right one for eigenvalue problems, we show that the patch reconstructed approximate space attains the same accuracy with much less degree of freedoms than classical discontinuous Galerkin methods.
Revised:  To justify that our method is the right one for eigenvalue problems, we show that the patch reconstructed approximate space attains the same accuracy with fewer degrees of freedom than classical discontinuous Galerkin methods.
Edit intent: clarity
Original:  With order increasing , our method can even possess better performances than conforming finite element methods, which are traditionally the  choice to solve problems with high regularities.
Revised:  With order increasing , our method can even achieve a better performance than conforming finite element methods, which are traditionally the choice to solve problems with high regularities.
Edit intent: clarity
Original:  With order increasing , our method can even possess better performances than conforming finite element methods, which are traditionally the  choice to solve problems with high regularities.
Revised:  With order increasing , our method can even possess better performances than conforming finite element methods, such methods are traditionally the choice to solve problems with high regularities.
Edit intent: clarity