wanyu/IteraTeR_v2 huggingface dataset:
Original:  Specifically, we consider homogeneous spheres of stochastic neo-Hookean material, composites with two concentric stochastic neo-Hookean phases, and inhomogeneous spheres of neo-Hookean-like material with a radially varying parameter.
Revised:  Specifically, we consider homogeneous spheres of stochastic neo-Hookean material, composites with two concentric stochastic neo-Hookean phases, and inhomogeneous spheres of locally neo-Hookean material with a radially varying parameter.
Edit intent: clarity
Original:  When these spheres are subject to a uniform tensile surface dead load in the radial direction , we show that the material at the centre determines the critical load at which a spherical cavity forms there .
Revised:  In all cases , we show that the material at the centre determines the critical load at which a spherical cavity forms there .
Edit intent: clarity
Original:  When these spheres are subject to a uniform tensile surface dead load in the radial direction , we show that the material at the centre determines the critical load at which a spherical cavity forms there .
Revised:  When these spheres are subject to a uniform tensile surface dead load in the radial direction , we show that the material at the centre determines the critical load at which a spherical cavity forms .
Edit intent: clarity
Original:  However, while  supercritical bifurcation, with stable cavitation, is always obtained in a static sphere of stochastic neo-Hookean material, for the composite and radially inhomogeneous spheres, a subcritical bifurcation, with snap cavitation, is also possible.
Revised:  However, while supercritical bifurcation, with stable cavitation, is obtained in a static sphere of stochastic neo-Hookean material, for the composite and radially inhomogeneous spheres, a subcritical bifurcation, with snap cavitation, is also possible.
Edit intent: clarity
Original:  For the dynamic spheres under suitable dead-load traction , oscillatory motions are produced  , such that a cavity forms and expands to a maximum radius, then collapses again to zero and repeats the cycle.
Revised:  For the dynamic spheres , oscillatory motions are produced , such that a cavity forms and expands to a maximum radius, then collapses again to zero and repeats the cycle.
Edit intent: clarity
Original:  For the dynamic spheres under suitable dead-load traction , oscillatory motions are produced  , such that a cavity forms and expands to a maximum radius, then collapses again to zero and repeats the cycle.
Revised:  For the dynamic spheres under suitable dead-load traction , oscillatory motions are produced under suitable dead-load traction , such that a cavity forms and expands to a maximum radius, then collapses again to zero and repeats the cycle.
Edit intent: fluency
Original:  As the material parameters are non-deterministic , the results are characterised by probability distributions.
Revised:  As the material parameters are non-deterministic , the results can be characterised in terms of probability distributions.
Edit intent: clarity
Original:  In all cases, we show that the material at the centre determines the critical load at which a spherical cavity forms  .
Revised:  In all cases, we show that the material at the centre determines the critical load at which a spherical cavity forms there .
Edit intent: clarity
Original:  Numerical results show that AMG-DD achieves superior accuracy per communication cost compared to AMG, indicating that it should provide significant speedups for computational environments where the cost of communication is high compared to the cost of computation, such as very large clusters or GPU accelerated systems .
Revised:  Numerical results show that AMG-DD achieves superior accuracy per communication cost compared to AMG, and speedup over AMG is demonstrated on a large GPU cluster .
Edit intent: clarity
Original:  We also demonstrate the method on a model equation as well as on the simulation of elastic and viscoelastic wave propagation.
Revised:  We demonstrate the method on a model equation as well as on the simulation of elastic and viscoelastic wave propagation.
Edit intent: clarity
Original: In this paper we describe a method for removing the numerical errors in the modeling of linear evolution equations that are caused by approximating the time derivative by a finite difference operator.
Revised: We describe a method for removing the numerical errors in the modeling of linear evolution equations that are caused by approximating the time derivative by a finite difference operator.
Edit intent: coherence
Original:  The method is based on integral transforms realized as certain Fourier integral operators,  and we prove that  under an assumption on the frequency support it results in a solution with correct evolution throughout the entire lifespan.
Revised:  The method is based on integral transforms realized as certain Fourier integral operators, and we prove that , under an assumption on the frequency support it results in a solution with correct evolution throughout the entire lifespan.
Edit intent: fluency
Original:  The method is based on integral transforms realized as certain Fourier integral operators,  and we prove that  under an assumption on the frequency support it results in a solution with correct evolution throughout the entire lifespan.
Revised:  The method is based on integral transforms realized as certain Fourier integral operators, and we prove that under an assumption about the frequency content, it yields a solution with correct evolution throughout the entire lifespan.
Edit intent: clarity
Original:  We propose a computational framework to allow multiple components to interact in different modes  , exchange information, adapt their behaviour, and reconfigure their communication interfaces.
Revised:  We propose a computational framework to allow multiple components to interact in different modes , adapt their behaviour, and reconfigure their communication interfaces.
Edit intent: clarity
Original:  The framework permits a local interaction based on shared variables and a global one based on message passing.
Revised:  The formalism defines a local behaviour based on shared variables and a global one based on message passing.
Edit intent: clarity
Original:  To be able to reason about local and global behaviour, we extend LTL to consider the exchanged messages and their constraints.
Revised:  We extend LTL to be able to reason about local and global behaviour, we extend LTL to consider the exchanged messages and their constraints.
Edit intent: fluency
Original:  Finally, we study the computational complexity of satisfiability and verification considering these extensions .
Revised:  Finally, we study the computational complexity of satisfiability and model-checking of this extension .
Edit intent: clarity
Original: In this paper , we propose a novel efficient algorithm for calculating winding numbers, aiming at counting the number of roots of a given polynomial in a convex region on the complex plane.
Revised: In this paper we propose a novel efficient algorithm for calculating winding numbers, aiming at counting the number of roots of a given polynomial in a convex region on the complex plane.
Edit intent: fluency
Original:  This algorithm can be used for counting and exclusion tests in a subdivision algorithms for polynomial root-fnding , and would be especially useful in application scenarios where high-precision polynomial cofficients are hard to obtain but we succeed with counting already by using polynomial evaluation with lower precision.
Revised:  This algorithm can be used for counting and exclusion tests in a subdivision algorithms for polynomial root-finding , and would be especially useful in application scenarios where high-precision polynomial cofficients are hard to obtain but we succeed with counting already by using polynomial evaluation with lower precision.
Edit intent: fluency
Original:  This algorithm can be used for counting and exclusion tests in a subdivision algorithms for polynomial root-fnding , and would be especially useful in application scenarios where high-precision polynomial cofficients are hard to obtain but we succeed with counting already by using polynomial evaluation with lower precision.
Revised:  This algorithm can be used for counting and exclusion tests in a subdivision algorithms for polynomial root-fnding , and would be especially usefull in application scenarios where high-precision polynomial cofficients are hard to obtain but we succeed with counting already by using polynomial evaluation with lower precision.
Edit intent: fluency
Original:  This algorithm can be used for counting and exclusion tests in a subdivision algorithms for polynomial root-fnding , and would be especially useful in application scenarios where high-precision polynomial cofficients are hard to obtain but we succeed with counting already by using polynomial evaluation with lower precision.
Revised:  This algorithm can be used for counting and exclusion tests in a subdivision algorithms for polynomial root-fnding , and would be especially useful in application scenarios where high-precision polynomial coefficients are hard to obtain but we succeed with counting already by using polynomial evaluation with lower precision.
Edit intent: fluency
Original:  We provide the pseudo code of the algorithm  as well as a proof of its correctness .
Revised:  We provide the pseudo code of the algorithm , proof of its correctness as well as a proof of its correctness .
Edit intent: fluency
Original:  2 ) Does a hard-on-average language in NP imply a hard problem in TFNP (i.e., the class of total NP search problem)?
Revised:  2 ) Does a hard-on-average language in NP imply a hard-on-average problem in TFNP (i.e., the class of total NP search problem)?
Edit intent: fluency
Original:  We show that the answer to (at least) one of these questions is yes.
Revised:  Our main result is that the answer to (at least) one of these questions is yes.
Edit intent: clarity
Original:  In other words, in Impagliazzo's Pessiland (where NP is hard-on-average, but one-way functions do not exist), TFNP is unconditionally hard (on average) .
Revised:  Both one-way functions do not exist), TFNP is unconditionally hard (on average) .
Edit intent: coherence
Original:  This result follows from a more general theory of interactive average-case complexity, and in particular, a novel round-collapse theorem for computationally-sound protocols, analogous to Babai-Moran's celebrated round-collapse theorem for information-theoretically sound protocols.
Revised:  This result follows from a more general study of interactive puzzles---a generalization of average-case complexity, and in particular, a novel round-collapse theorem for computationally-sound protocols, analogous to Babai-Moran's celebrated round-collapse theorem for information-theoretically sound protocols.
Edit intent: clarity
Original: In a reduced graph 1%DIFDELCMD < ]%%% , a I cycle-set is the    set of cycles only connected by interior points . |I| is the number of I cycle-sets in a given graph.
Revised:  1%DIFDELCMD < ]%%% , a I cycle-set is the set of cycles only connected by interior points . |I| is the number of I cycle-sets in a given graph.
Edit intent: clarity
Original: In a reduced graph 1%DIFDELCMD < ]%%% , a I cycle-set is the    set of cycles only connected by interior points . |I| is the number of I cycle-sets in a given graph.
Revised: In a reduced graph %DIFDELCMD < ]%%% , a I cycle-set is the set of cycles only connected by interior points . |I| is the number of I cycle-sets in a given graph.
Edit intent: clarity
Original: In a reduced graph 1%DIFDELCMD < ]%%% , a I cycle-set is the    set of cycles only connected by interior points . |I| is the number of I cycle-sets in a given graph.
Revised: In a reduced graph 1%DIFDELCMD < ]%%% A graph set of cycles only connected by interior points . |I| is the number of I cycle-sets in a given graph.
Edit intent: clarity
Original: In a reduced graph 1%DIFDELCMD < ]%%% , a I cycle-set is the    set of cycles only connected by interior points . |I| is the number of I cycle-sets in a given graph.
Revised: In a reduced graph 1%DIFDELCMD < ]%%% , a I cycle-set is the , set of cycles only connected by interior points . |I| is the number of I cycle-sets in a given graph.
Edit intent: fluency
Original: In a reduced graph 1%DIFDELCMD < ]%%% , a I cycle-set is the    set of cycles only connected by interior points . |I| is the number of I cycle-sets in a given graph.
Revised: In a reduced graph 1%DIFDELCMD < ]%%% , a I cycle-set is the set of cycles only jointed by inside vertices . |I| is the number of I cycle-sets in a given graph.
Edit intent: clarity
Original: In a reduced graph 1%DIFDELCMD < ]%%% , a I cycle-set is the    set of cycles only connected by interior points . |I| is the number of I cycle-sets in a given graph.
Revised: In a reduced graph 1%DIFDELCMD < ]%%% , a I cycle-set is the set of cycles only connected by interior points . |I| is the number of sets I in a graph.
Edit intent: clarity
Original:  \mathcal{g \textit{  .
Revised:  \mathcal{g \textit{g .
Edit intent: fluency
Original:  In this paper, we present a theorem that a graph G\textit{ is non-Hamiltonian, if and only if, \mathcal{g \textit{ and K_2 ,3 are homeomorphic.
Revised:  In this paper, we present a theorem that a graph G\textit{ is non-Hamiltonian, if and only if, \textit{ and K_2 ,3 are homeomorphic.
Edit intent: coherence
Original:  This feature  provides an approximation that is scalable with respect to the sample size.
Revised:  This feature naturally provides an approximation that is scalable with respect to the sample size.
Edit intent: clarity
Original:  The new density estimator has unitary integral, does not require a constraint to enforce positivity, and is consistent.
Revised:  The proposed density estimator has unitary integral, does not require a constraint to enforce positivity, and is consistent.
Edit intent: clarity
Original:  The new approach is validated through numerical examples in which samples are drawn from known PDFs.
Revised:  The proposed approach is validated through numerical examples in which samples are drawn from known PDFs.
Edit intent: clarity
Original:  FatPaths enables state-of-the-art low-diameter topologies such as Slim Fly to achieve unprecedented performance , targeting both HPC supercomputers as well as  data centers and clusters used by cloud computing .
Revised:  FatPaths enables state-of-the-art low-diameter topologies such as Slim Fly to achieve unprecedented performance , targeting both HPC supercomputers as well as cloud data centers and clusters used by cloud computing .
Edit intent: fluency
Original:  FatPaths enables state-of-the-art low-diameter topologies such as Slim Fly to achieve unprecedented performance , targeting both HPC supercomputers as well as  data centers and clusters used by cloud computing .
Revised:  FatPaths enables state-of-the-art low-diameter topologies such as Slim Fly to achieve unprecedented performance , targeting both HPC supercomputers as well as data centers and clusters .
Edit intent: clarity
Original:  Moreover, FatPaths features a redesigned "purified" transport layer , based on recent advances in data center networking, that removes virtually all TCP performance issues (e.g., the slow start) .
Revised:  Moreover, FatPaths uses a redesigned "purified" transport layer , based on recent advances in data center networking, that removes virtually all TCP performance issues (e.g., the slow start) .
Edit intent: clarity
Original:  Moreover, FatPaths features a redesigned "purified" transport layer , based on recent advances in data center networking, that removes virtually all TCP performance issues (e.g., the slow start) .
Revised:  Moreover, FatPaths features a redesigned "purified" transport layer that removes virtually all TCP performance issues (e.g., the slow start) .
Edit intent: clarity
Original: We describe a general approach to obtain dual representations for systemic risk measures of the "allocate first, then aggregate"-type, which have recently received significant attention in the literature.
Revised: We establish dual representations for systemic risk measures of the "allocate first, then aggregate"-type, which have recently received significant attention in the literature.
Edit intent: clarity
Original:  As a final application, we apply our results to derive a simple proof of the dual representation of univariate utility-based risk measures  .
Revised:  As a final application, we apply our results to derive a simple proof of the dual representation of utility-based risk measures .
Edit intent: clarity
Original:  Before solving a problem on D-Wave, several preprocessing methods can be applied, one of them being the so-called spin reversal or gauge transform.
Revised:  Before solving a problem on D-Wave, several pre-processing methods can be applied, one of them being the so-called spin reversal or gauge transform.
Edit intent: fluency
Original:  Recently, Graph Neural Network ( GNN) is proposed as a general and powerful framework to handle tasks on graph data, e.g., node embedding, link prediction and node classification.
Revised:  Recently, Graph Neural Network ( GNNs) are proposed as a general and powerful framework to handle tasks on graph data, e.g., node embedding, link prediction and node classification.
Edit intent: clarity
Original:  As a representative implementation of GNNs, Graph Attention Networks ( GAT) is successfully applied in a variety of tasks on real datasets.
Revised:  As a representative implementation of GNNs, Graph Attention Networks ( GATs) are successfully applied in a variety of tasks on real datasets.
Edit intent: fluency
Original:  In this paper, we propose Signed Graph Attention Networks ( SiGAT ), generalizing GAT to signed networks.
Revised:  In this paper, we propose Signed Graph Attention Networks ( SiGATs ), generalizing GAT to signed networks.
Edit intent: clarity
Original:  Experimental results on three real datasets demonstrate that SiGAT outperforms feature-based method, network embedding method and state-of-the-art GNN-based methods like signed graph convolutional networks (SGCN).
Revised:  Experimental results on three real datasets demonstrate that SiGAT outperforms feature-based method, network embedding method and state-of-the-art GNN-based methods like signed graph convolutional network (SGCN).
Edit intent: fluency
Original:  A key obstacle is the forbiddingly high dimensionality of the resulting stochastic epidemicmodel.
Edit intent: coherence
Original:  Using systematic simulations , we propose a parsimonious (three-parameter) model of these rates and  show that different wellknown network families map onto distinct regions of the parameter space of this model.
Revised:  Using systematic simulations , we propose a parsimonious (three-parameter) model of these rates and show that different well-known network classes map onto distinct regions of the parameter space of this model.
Edit intent: clarity
Original:  We show that the proposed methodology yields excellent results when tested on synthetic and real-world networks .
Revised:  We show that the proposed methodology yields good results on both synthetic and real-world networks .
Edit intent: clarity
Original:  These networks can be deployed by traditional mobile network operators (MNOs) or entrant local micro-operators .
Revised:  These networks can be deployed by traditional mobile network operators or entrant local micro-operators .
Edit intent: clarity
Original:  These networks can be deployed by traditional mobile network operators (MNOs) or entrant local micro-operators .
Revised:  These networks can be deployed by traditional mobile network operators (MNOs) or entrant local operators .
Edit intent: clarity
Original:  Network slicing will enable a single local 5G micro-operator network to efficiently serve the multiple verticals and their tenants with different network requirements.
Revised:  Network slicing will enable a 5G micro-operator network to efficiently serve the multiple verticals and their tenants with different network requirements.
Edit intent: clarity
Original:  The paper proposes  descriptive technique by which different network slicing management functionalities such as the Network Slice Management Function (NSMF), Network Slice Subnet Management Function (NSSMF) and Communication Service Management Function (CSMF) can be used in coordination to create, orchestrate and manage network slicing for different deployment scenario of a micro-operator  based on the Network Slice instance (NSI) configuration type that can exist for each scenario.
Revised:  The paper proposes a descriptive technique by which different network slicing management functionalities such as the Network Slice Management Function (NSMF), Network Slice Subnet Management Function (NSSMF) and Communication Service Management Function (CSMF) can be used in coordination to create, orchestrate and manage network slicing for different deployment scenario of a micro-operator based on the Network Slice instance (NSI) configuration type that can exist for each scenario.
Edit intent: fluency
Original:  The paper proposes  descriptive technique by which different network slicing management functionalities such as the Network Slice Management Function (NSMF), Network Slice Subnet Management Function (NSSMF) and Communication Service Management Function (CSMF) can be used in coordination to create, orchestrate and manage network slicing for different deployment scenario of a micro-operator  based on the Network Slice instance (NSI) configuration type that can exist for each scenario.
Revised:  The paper proposes descriptive technique by which different network slicing management functionalities such as the Network Slice Management Function (NSMF), Network Slice Subnet Management Function (NSSMF) and Communication Service Management Function (CSMF) can be used in coordination to create, orchestrate and manage network slicing for different deployment scenarios of a micro-operator based on the Network Slice instance (NSI) configuration type that can exist for each scenario.
Edit intent: fluency
Original:  The paper proposes  descriptive technique by which different network slicing management functionalities such as the Network Slice Management Function (NSMF), Network Slice Subnet Management Function (NSSMF) and Communication Service Management Function (CSMF) can be used in coordination to create, orchestrate and manage network slicing for different deployment scenario of a micro-operator  based on the Network Slice instance (NSI) configuration type that can exist for each scenario.
Revised:  The paper proposes descriptive technique by which different network slicing management functionalities such as the Network Slice Management Function (NSMF), Network Slice Subnet Management Function (NSSMF) and Communication Service Management Function (CSMF) can be used in coordination to create, orchestrate and manage network slicing for different deployment scenario of a micro-operator . This is based on the Network Slice instance (NSI) configuration type that can exist for each scenario.
Edit intent: coherence
Original:  The paper proposes  descriptive technique by which different network slicing management functionalities such as the Network Slice Management Function (NSMF), Network Slice Subnet Management Function (NSSMF) and Communication Service Management Function (CSMF) can be used in coordination to create, orchestrate and manage network slicing for different deployment scenario of a micro-operator  based on the Network Slice instance (NSI) configuration type that can exist for each scenario.
Revised:  The paper proposes descriptive technique by which different network slicing management functionalities such as the Network Slice Management Function (NSMF), Network Slice Subnet Management Function (NSSMF) and Communication Service Management Function (CSMF) can be used in coordination to create, orchestrate and manage network slicing for different deployment scenario of a micro-operator based on the network slice instance configuration type that can exist for each scenario.
Edit intent: clarity