wanyu/IteraTeR_v2 huggingface dataset:
Original:  The one of the key ideas of stochastic network calculus is the possibility to describe service offered at network node as  stochastic service envelope, which in turn can be used to describe the stochastic service available in a network of nodes and determine end-to-end probabilistic delay and backlog bounds.
Revised:  The one of the key ideas of stochastic network calculus is the possibility to describe service offered at network node as a stochastic service envelope, which in turn can be used to describe the stochastic service available in a network of nodes and determine end-to-end probabilistic delay and backlog bounds.
Edit intent: fluency
Original:  It is shown for (\sigma(\theta), \rho(\theta)) - constrained traffic model that the end-to-end performance measures computed using the new stochastic network service envelope are tight in comparison with the ones obtained using the existing start-of-the-art definition of statistical network service envelope and are bounded by {\cal O}(H H), where H is the number of nodes traversed by the arrival traffic.
Revised:  It is shown for (\sigma(\theta), \rho(\theta)) - constrained traffic model that the end-to-end performance measures computed using the new stochastic network service envelope are tight in comparison to the ones obtained using the existing start-of-the-art definition of statistical network service envelope and are bounded by {\cal O}(H H), where H is the number of nodes traversed by the arrival traffic.
Edit intent: fluency
Original:  Such a fractal is obtained as the Hausdorff limit of a sequence of compact planar sets, where each set is the projection of a finite union of faces of unit cubes generated by a multidimensional version of the underlying Arnoux-Rauzy substitution.
Edit intent: coherence
Original: With the current hybridization of treecodes and FMMs, combined with auto-tuning capabilities on heterogeneous architectures, the flexibility of fast N -body methods has been greatly enhanced.
Revised: With the current hybridization of treecodes and FMMs, combined with auto-tuning capabilities on heterogeneous architectures, the flexibility of fast N-body methods has been greatly enhanced.
Edit intent: fluency
Original:  These features are a requirement to developing a black- box software library for fast N-body algorithms on heterogeneous systems, which is our immediate goal.
Revised:  These features are a requirement to developing a black-box software library for fast N-body algorithms on heterogeneous systems, which is our immediate goal.
Edit intent: fluency
Original:  In implicitization, it computes the polytope of a bicubic surface in 3 \mu%DIFDELCMD < }%%% sec, whereas computing the secondary polytope is not feasible on the same computer.
Revised:  In implicitization, it computes the polytope of \mu%DIFDELCMD < }%%% sec, whereas computing the secondary polytope is not feasible on the same computer.
Edit intent: clarity
Original:  In implicitization, it computes the polytope of a bicubic surface in 3 \mu%DIFDELCMD < }%%% sec, whereas computing the secondary polytope is not feasible on the same computer.
Revised:  In implicitization, it computes the polytope of a bicubic surface in 3 %DIFDELCMD < }%%% sec, whereas computing the secondary polytope is not feasible on the same computer.
Edit intent: fluency
Original:  Given the Newton polytopes of n+1 polynomials in n variables Cayley trick defines pointset A\subset%DIFDELCMD < \Z%%% ^{2n.
Revised:  %DIFDELCMD < \Z%%% ^{2n.
Edit intent: coherence
Original:  The code is based on experimental CGAL package triangulation , and yields a triangulation of the polytope, useful for the targeted applications .
Revised:  The code is based on experimental CGAL package triangulation .
Edit intent: clarity
Original:  A variant  computes successively tighter inner and outer approximations: typically, these polytopes have, respectively, 90\% and 105\% of the true volume, while runtime is reduced up to 25 times.
Revised:  A variant of the algorithm computes successively tighter inner and outer approximations: typically, these polytopes have, respectively, 90\% and 105\% of the true volume, while runtime is reduced up to 25 times.
Edit intent: clarity
Original:  A variant  computes successively tighter inner and outer approximations: typically, these polytopes have, respectively, 90\% and 105\% of the true volume, while runtime is reduced up to 25 times.
Revised:  A variant computes successively tighter inner and outer approximations: when these polytopes have, respectively, 90\% and 105\% of the true volume, while runtime is reduced up to 25 times.
Edit intent: clarity
Original:  A variant  computes successively tighter inner and outer approximations: typically, these polytopes have, respectively, 90\% and 105\% of the true volume, while runtime is reduced up to 25 times.
Revised:  A variant computes successively tighter inner and outer approximations: typically, these polytopes have, respectively, 90\% and 105\% of the true volume, runtime is reduced up to 25 times.
Edit intent: coherence
Original:  The resultant is fundamental in elimination, and in implicitizing parametric hypersurfaces: we compute the polytope of surface equations in <1sec, assuming <100 terms in parametric polynomials, which includes all common instances in geometric modeling, whereas the corresponding \Sigma(A) are intractable.
Edit intent: coherence
Original:  Our method computes instances of 5, 6, 7-dimensional polytopes with 35K, 23K , 500 vertices, respectively, in < 2hr , and should yield an efficient algorithm for interpolating resultants . Compared to tropical geometry code , ours is faster up to dimensions 5 , 6, and competitive in higher dimensions . Compared to lrs,cdd,polymake in its convex hull step, it is fastest along with polymake .
Revised:  Our method computes instances of 5-, 6- or 7-dimensional polytopes with 35K, 23K , 500 vertices, respectively, in < 2hr , and should yield an efficient algorithm for interpolating resultants . Compared to tropical geometry code , ours is faster up to dimensions 5 , 6, and competitive in higher dimensions . Compared to lrs,cdd,polymake in its convex hull step, it is fastest along with polymake .
Edit intent: coherence
Original:  Our method computes instances of 5, 6, 7-dimensional polytopes with 35K, 23K , 500 vertices, respectively, in < 2hr , and should yield an efficient algorithm for interpolating resultants . Compared to tropical geometry code , ours is faster up to dimensions 5 , 6, and competitive in higher dimensions . Compared to lrs,cdd,polymake in its convex hull step, it is fastest along with polymake .
Revised:  Our method computes instances of 5, 6, 7-dimensional polytopes with 35K, 23K or 500 vertices, respectively, in < 2hr , and should yield an efficient algorithm for interpolating resultants . Compared to tropical geometry code , ours is faster up to dimensions 5 , 6, and competitive in higher dimensions . Compared to lrs,cdd,polymake in its convex hull step, it is fastest along with polymake .
Edit intent: clarity
Original:  Our method computes instances of 5, 6, 7-dimensional polytopes with 35K, 23K , 500 vertices, respectively, in < 2hr , and should yield an efficient algorithm for interpolating resultants . Compared to tropical geometry code , ours is faster up to dimensions 5 , 6, and competitive in higher dimensions . Compared to lrs,cdd,polymake in its convex hull step, it is fastest along with polymake .
Revised:  Our method computes instances of 5, 6, 7-dimensional polytopes with 35K, 23K , 500 vertices, resp., within 2hr , and should yield an efficient algorithm for interpolating resultants . Compared to tropical geometry code , ours is faster up to dimensions 5 , 6, and competitive in higher dimensions . Compared to lrs,cdd,polymake in its convex hull step, it is fastest along with polymake .
Edit intent: clarity
Original:  Our method computes instances of 5, 6, 7-dimensional polytopes with 35K, 23K , 500 vertices, respectively, in < 2hr , and should yield an efficient algorithm for interpolating resultants . Compared to tropical geometry code , ours is faster up to dimensions 5 , 6, and competitive in higher dimensions . Compared to lrs,cdd,polymake in its convex hull step, it is fastest along with polymake .
Revised:  Our method computes instances of 5, 6, 7-dimensional polytopes with 35K, 23K , 500 vertices, respectively, in < 2hr . Compared to tropical geometry code , ours is faster up to dimensions 5 , 6, and competitive in higher dimensions . Compared to lrs,cdd,polymake in its convex hull step, it is fastest along with polymake .
Edit intent: coherence
Original:  Our method computes instances of 5, 6, 7-dimensional polytopes with 35K, 23K , 500 vertices, respectively, in < 2hr , and should yield an efficient algorithm for interpolating resultants . Compared to tropical geometry code , ours is faster up to dimensions 5 , 6, and competitive in higher dimensions . Compared to lrs,cdd,polymake in its convex hull step, it is fastest along with polymake .
Revised:  Our method computes instances of 5, 6, 7-dimensional polytopes with 35K, 23K , 500 vertices, respectively, in < 2hr , and should yield an efficient algorithm for interpolating resultants . Compared to tropical geometry software , ours is faster up to dimensions 5 , 6, and competitive in higher dimensions . Compared to lrs,cdd,polymake in its convex hull step, it is fastest along with polymake .
Edit intent: clarity
Original:  Our method computes instances of 5, 6, 7-dimensional polytopes with 35K, 23K , 500 vertices, respectively, in < 2hr , and should yield an efficient algorithm for interpolating resultants . Compared to tropical geometry code , ours is faster up to dimensions 5 , 6, and competitive in higher dimensions . Compared to lrs,cdd,polymake in its convex hull step, it is fastest along with polymake .
Revised:  Our method computes instances of 5, 6, 7-dimensional polytopes with 35K, 23K , 500 vertices, respectively, in < 2hr , and should yield an efficient algorithm for interpolating resultants . Compared to tropical geometry code , ours is faster up to dimension 5 , 6, and competitive in higher dimensions . Compared to lrs,cdd,polymake in its convex hull step, it is fastest along with polymake .
Edit intent: fluency
Original:  Our method computes instances of 5, 6, 7-dimensional polytopes with 35K, 23K , 500 vertices, respectively, in < 2hr , and should yield an efficient algorithm for interpolating resultants . Compared to tropical geometry code , ours is faster up to dimensions 5 , 6, and competitive in higher dimensions . Compared to lrs,cdd,polymake in its convex hull step, it is fastest along with polymake .
Revised:  Our method computes instances of 5, 6, 7-dimensional polytopes with 35K, 23K , 500 vertices, respectively, in < 2hr , and should yield an efficient algorithm for interpolating resultants . Compared to tropical geometry code , ours is faster up to dimensions 5 or 6, and competitive in higher dimensions . Compared to lrs,cdd,polymake in its convex hull step, it is fastest along with polymake .
Edit intent: clarity
Original: We develop an incremental algorithm to compute the Newton polytope of the resultant, aka resultant polytope, or its  projection along a given direction.
Revised: We design an algorithm to compute the Newton polytope of the resultant, aka resultant polytope, or its projection along a given direction.
Edit intent: clarity
Original: We develop an incremental algorithm to compute the Newton polytope of the resultant, aka resultant polytope, or its  projection along a given direction.
Revised: We develop an incremental algorithm to compute the Newton polytope of the resultant, known as resultant polytope, or its projection along a given direction.
Edit intent: fluency
Original:  The resultant is fundamental in algebraic elimination and in implicitization of parametric hypersurfaces .
Revised:  The resultant is fundamental in algebraic elimination , optimization, and geometric modeling .
Edit intent: clarity
Original:  Our algorithm exactly computes vertex- and halfspace-representations of the desired polytope using an oracle producing resultant vertices in a given direction .
Revised:  Our algorithm exactly computes vertex- and halfspace-representations of the polytope using an oracle producing resultant vertices in a given direction .
Edit intent: clarity
Original:  It is output-sensitive as it uses one oracle call per vertex .
Revised:  It is output-sensitive as it makes one oracle call per vertex .
Edit intent: clarity
Original:  A variant of the algorithm computes successively tighter inner and outer approximations: when these polytopes have, respectively, 90\% and 105\% of the true volume, runtime is reduced up to 25 times.
Edit intent: coherence
Original:  Our method computes instances of 5-, 6- or 7-dimensional polytopes with 35K, 23K or 500 vertices, resp., within 2hr.
Revised:  Our method computes 5-, 6- or 7-dimensional polytopes with 35K, 23K or 500 vertices, resp., within 2hr.
Edit intent: clarity
Original:  Our method computes instances of 5-, 6- or 7-dimensional polytopes with 35K, 23K or 500 vertices, resp., within 2hr.
Revised:  Our method computes instances of 5-, 6- and 7-dimensional polytopes with 35K, 23K or 500 vertices, resp., within 2hr.
Edit intent: fluency
Original:  Our method computes instances of 5-, 6- or 7-dimensional polytopes with 35K, 23K or 500 vertices, resp., within 2hr.
Revised:  Our method computes instances of 5-, 6- or 7-dimensional polytopes with 35K, 23K and 500 vertices, resp., within 2hr.
Edit intent: fluency
Original:  Compared to tropical geometry software , ours is faster up to dimension 5 or 6, and competitive in higher dimensions .
Revised:  Compared to tropical geometry software up to dimension 5 or 6, and competitive in higher dimensions .
Edit intent: clarity
Original:  This raises the question of whether there is a nontrivial class of network topologies for which achievability is always equivalent to "routability" , for any combination of source signals and positive channel capacities.
Revised:  This raises the question of whether there is a nontrivial class of network topologies for which achievability is always equivalent to 'routability' , for any combination of source signals and positive channel capacities.
Edit intent: fluency
Original:  This paper considers possibly cyclic, directed, errorless networks with n source-sink pairs , mutually independent source signals , and a relaxed communication objective in terms of demanded information rates at sinks .
Revised:  This chapter considers possibly cyclic, directed, errorless networks with n source-sink pairs , mutually independent source signals , and a relaxed communication objective in terms of demanded information rates at sinks .
Edit intent: clarity
Original:  This paper considers possibly cyclic, directed, errorless networks with n source-sink pairs , mutually independent source signals , and a relaxed communication objective in terms of demanded information rates at sinks .
Revised:  This paper considers possibly cyclic, directed, errorless networks with n source-sink pairs and mutually independent source signals , and a relaxed communication objective in terms of demanded information rates at sinks .
Edit intent: fluency
Original:  This paper considers possibly cyclic, directed, errorless networks with n source-sink pairs , mutually independent source signals , and a relaxed communication objective in terms of demanded information rates at sinks .
Revised:  This paper considers possibly cyclic, directed, errorless networks with n source-sink pairs , mutually independent source signals .
Edit intent: clarity
Original:  The concept of triangularizability is introduced , and it is shown that  if the network topology is triangularizable then a given combination of source signals, demand rates and channel capacities is achievable if and only if the digraph supports a feasible multicommodity flow  .
Revised:  The concept of is introduced , and it is shown that if the network topology is triangularizable then a given combination of source signals, demand rates and channel capacities is achievable if and only if the digraph supports a feasible multicommodity flow .
Edit intent: clarity
Original:  The concept of triangularizability is introduced , and it is shown that  if the network topology is triangularizable then a given combination of source signals, demand rates and channel capacities is achievable if and only if the digraph supports a feasible multicommodity flow  .
Revised:  The concept of triangularizability is introduced , and it is shown that , if the network topology is triangularizable then a given combination of source signals, demand rates and channel capacities is achievable if and only if the digraph supports a feasible multicommodity flow .
Edit intent: fluency
Original:  The concept of triangularizability is introduced , and it is shown that  if the network topology is triangularizable then a given combination of source signals, demand rates and channel capacities is achievable if and only if the digraph supports a feasible multicommodity flow  .
Revised:  The concept of triangularizability is introduced , and it is shown that if the network topology is downward matched, then a given combination of source signals, demand rates and channel capacities is achievable if and only if the digraph supports a feasible multicommodity flow .
Edit intent: clarity
Original:  The concept of triangularizability is introduced , and it is shown that  if the network topology is triangularizable then a given combination of source signals, demand rates and channel capacities is achievable if and only if the digraph supports a feasible multicommodity flow  .
Revised:  The concept of triangularizability is introduced , and it is shown that if the network topology is triangularizable then a given combination of source signals, demand rates and channel capacities is achievable if and only if there is a feasible multicommodity flow .
Edit intent: clarity
Original:  Several examples are analysed, including the butterfly network and directed cycles .
Revised:  Several examples are analysed, including the butterfly network and directed lines .
Edit intent: clarity
Original:  This raises the question of whether there is a nontrivial class of network topologies for which achievability is always equivalent to 'routability' , for any combination of source signals and positive channel capacities.
Revised:  This raises the question of whether there is a nontrivial class of network topologies for which achievability is always equivalent to routability , for any combination of source signals and positive channel capacities.
Edit intent: fluency
Original:  The concept of 'downward matching' is introduced and it is shown that, if the network topology is downward matched, then a given combination of source signals , demand rates and channel capacities is achievable if and only if there is a feasible multicommodity flow .
Revised:  The concept of downward dominance is introduced and it is shown that, if the network topology is downward matched, then a given combination of source signals , demand rates and channel capacities is achievable if and only if there is a feasible multicommodity flow .
Edit intent: clarity
Original:  The concept of 'downward matching' is introduced and it is shown that, if the network topology is downward matched, then a given combination of source signals , demand rates and channel capacities is achievable if and only if there is a feasible multicommodity flow .
Revised:  The concept of 'downward matching' is introduced and it is shown that, if the network topology is downward dominated, then the achievability of a given combination of source signals , demand rates and channel capacities is achievable if and only if there is a feasible multicommodity flow .
Edit intent: clarity
Original:  The concept of 'downward matching' is introduced and it is shown that, if the network topology is downward matched, then a given combination of source signals , demand rates and channel capacities is achievable if and only if there is a feasible multicommodity flow .
Revised:  The concept of 'downward matching' is introduced and it is shown that, if the network topology is downward matched, then a given combination of source signals and channel capacities is achievable if and only if there is a feasible multicommodity flow .
Edit intent: clarity
Original:  The concept of 'downward matching' is introduced and it is shown that, if the network topology is downward matched, then a given combination of source signals , demand rates and channel capacities is achievable if and only if there is a feasible multicommodity flow .
Revised:  The concept of 'downward matching' is introduced and it is shown that, if the network topology is downward matched, then a given combination of source signals , demand rates and channel capacities implies the existence of a feasible multicommodity flow .
Edit intent: clarity
Original: Tensor decomposition is a powerful  tool for multiway data analysis.
Revised: Tensor decomposition is a powerful computational tool for multiway data analysis.
Edit intent: clarity
Original:  Many popular tensor decomposition approaches---such as the Tucker decomposition and CANDECOMP/PARAFAC (CP) ---conduct multi-linear factorization.
Revised:  Many popular tensor decomposition approaches---such as the Tucker decomposition and CANDECOMP/PARAFAC (CP) ---amount to multi-linear factorization.
Edit intent: clarity
Original:  To address these issues, we propose a tensor-variate latent t process model, InfTucker, for robust multiway data analysis : it conducts robust Tucker decomposition in an infinite feature space.
Revised:  To address these issues, we propose tensor-variate latent t process model, InfTucker, for robust multiway data analysis : it conducts robust Tucker decomposition in an infinite feature space.
Edit intent: fluency
Original:  Unlike previous nonparametric Bayesian models on matrices and tensors, our latent t-process model focuses on multiway analysis and uses nonlinear covariance functions.
Revised:  Unlike previous Bayesian models on matrices and tensors, our latent t-process model focuses on multiway analysis and uses nonlinear covariance functions.
Edit intent: clarity
Original:  Unlike previous nonparametric Bayesian models on matrices and tensors, our latent t-process model focuses on multiway analysis and uses nonlinear covariance functions.
Revised:  Unlike previous nonparametric Bayesian models on matrices and tensors, our models are based on latent Gaussian or t processes with nonlinear covariance functions.
Edit intent: clarity
Original:  To efficiently learn  InfTucker from data, we develop a novel variational inference technique on tensors.
Revised:  To efficiently learn the InfTucker from data, we develop a novel variational inference technique on tensors.
Edit intent: fluency
Original:  To efficiently learn  InfTucker from data, we develop a novel variational inference technique on tensors.
Revised:  To efficiently learn InfTucker from data, we develop a variational inference technique on tensors.
Edit intent: clarity
Original:  This technique can be easily adopted in other contexts (e.g., multitask learning) where we encounter tensor-variate t processes or Gaussian processes.
Edit intent: coherence
Original:  Our experimental results on chemometrics and social network datasets demonstrate that the new InfTucker model achieves significantly higher prediction accuracy than several state-of-art tensor decomposition approaches including High Order Singular Value Decomposition (HOSVD), Weighted CP, and nonnegative tensor decomposition.
Revised:  Our experimental results on chemometrics and social network datasets demonstrate that our new models achieved significantly higher prediction accuracy than several state-of-art tensor decomposition approaches including High Order Singular Value Decomposition (HOSVD), Weighted CP, and nonnegative tensor decomposition.
Edit intent: clarity