wanyu/IteraTeR_full_sent huggingface dataset:
Original: This paper proposes a new method which approximates a classification function separating a d dimensional compact set into two parts . The approach starts by estimating the intersection between the classification boundary and the edges of a regular grid covering the compact set .
Revised: This paper proposes a new method which approximates a classification function separating a d dimensional compact set into two parts , and an efficient algorithm classifying points according to this approximation. In a first variant, the approximation is made of simplices that are defined in the cubes of a regular grid covering the compact set .
Edit intent: meaning-changed
Original:  The approach starts by estimating the intersection between the classification boundary and the edges of a regular grid covering the compact set . Then it builds a classification surface made of recursive simplex stars (resistars) defined in the grid cubescontaining such boundary points. A first variant, the simple resistar (s-resistar) defines a single star of simplices which share the barycentre of the cube boundary points and include stars of simplices defined similarly in cube facets, and so on recursively until a face boundary points define a single simplex.
Revised:  The approach starts by estimating the intersection between the classification boundary and the edges of a regular grid covering the compact set , from boundary points that approximate the intersection between M and the edges of the cubes. All the simplices defined in a cube share the barycentre of the cube boundary points and include stars of simplices defined similarly in cube facets, and so on recursively until a face boundary points define a single simplex.
Edit intent: clarity
Original:  A first variant, the simple resistar (s-resistar) defines a single star of simplices which share the barycentre of the cube boundary points and include stars of simplices defined similarly in cube facets, and so on recursively until a face boundary points define a single simplex.
Revised:  A first variant, the simple resistar (s-resistar) defines a single star of simplices which share the barycentre of the boundary points located in the cube and include simplices similarly defined in cube facets, and so on recursively until a face boundary points define a single simplex.
Edit intent: clarity
Original:  A first variant, the simple resistar (s-resistar) defines a single star of simplices which share the barycentre of the cube boundary points and include stars of simplices defined similarly in cube facets, and so on recursively until a face boundary points define a single simplex. This definition is simple and easy to apply when the dimensionality increases. However, s-resistars sometimes "glue" together surfaces that should be separated and this deteriorates the local classification performance. The second variant, the multi-boundary resistar (or m-resistar) addresses this problem by defining several simplex stars in a cube or in its faces when necessary, which is shown to increase the local classification performance.
Revised:  A first variant, the simple resistar (s-resistar) defines a single star of simplices which share the barycentre of the cube boundary points and include stars of simplices defined similarly in cube facets, and so on recursively . In a second variant, the Kuhn triangulation is used to break the cubes into simplices and the multi-boundary resistar (or m-resistar) addresses this problem by defining several simplex stars in a cube or in its faces when necessary, which is shown to increase the local classification performance.
Edit intent: meaning-changed
Original:  The second variant, the multi-boundary resistar (or m-resistar) addresses this problem by defining several simplex stars in a cube or in its faces when necessary, which is shown to increase the local classification performance. With both s-resistars and m-resistars, classifying a point  requires only a small number  of simple tests without explicitly computing the simplices.
Revised:  The second variant, the approximation is defined in these simplices from the boundary points computed on their edges, with the same principle. Both the approximation in cubes and in simplices define a separating surface on the whole grid and classifying a point requires only a small number of simple tests without explicitly computing the simplices.
Edit intent: meaning-changed
Original:  With both s-resistars and m-resistars, classifying a point  requires only a small number  of simple tests without explicitly computing the simplices. It is thus possible to use resistar classification in spaces of relatively high dimensionality (up to 9 in our tests) and for resistar surfaces including a large number of simplices (up to several trillions in our tests). The paper provides a theoretical argument and empirical evidence suggesting that, when the surface to approximate is smooth enough, the error of resistar classification decreases as \mathcal{O n_G^{-2}) for a grid of size n_G^d in d dimensions, whereas this error decreases as \mathcal{O .
Revised:  With both s-resistars and m-resistars, classifying a point requires only a small number of simple tests . Under some conditions on the definition of the boundary points and on the reach of M, for both variants the Hausdorff distance between M and its approximation decreases like \mathcal{O n_G^{-2}) for a grid of size n_G^d in d dimensions, whereas this error decreases as \mathcal{O .
Edit intent: meaning-changed
Original:  The paper provides a theoretical argument and empirical evidence suggesting that, when the surface to approximate is smooth enough, the error of resistar classification decreases as \mathcal{O n_G^{-2}) for a grid of size n_G^d in d dimensions, whereas this error decreases as \mathcal{O .
Revised:  The paper provides a theoretical argument and empirical evidence suggesting that, when the surface to approximate is smooth enough, the error of resistar classification decreases as \mathcal{O n_G^{-2}) , where n_G is the number of points on each axis of the grid. The approximation in cubes requires computing less boundary points than the approximation in simplices but the latter is always a manifold and is more accurate for a given value of n_G. The paper reports tests of the method when varying n_G and the dimensionality of the space (up to 9) .
Edit intent: meaning-changed
Original: We study equilibrium returns in a continuous-time model where heterogeneous mean-variance investors trade subject to quadratic transaction costs. The unique equilibrium is characterized by a system of coupled but linear forward-backward stochastic differential equations.
Revised: We study equilibrium returns in a continuous-time model where heterogeneous mean-variance investors trade subject to a quadratic transaction cost. The corresponding equilibrium is characterized by a system of coupled but linear forward-backward stochastic differential equations.
Edit intent: clarity
Original:  We assume that the motion of the motor is directly affected by the entropic barrier due to confinement when it is in the passive, unbound state, but not in the active, bound state . Confinement can further modulate the motor's binding kinetics.
Revised:  We assume that the motion of the MCC is directly affected by the entropic barrier due to confinement when it is in the passive, unbound state, but not in the active, bound state . Confinement can further modulate the motor's binding kinetics.
Edit intent: clarity
Original:  We assume that the motion of the motor is directly affected by the entropic barrier due to confinement when it is in the passive, unbound state, but not in the active, bound state . Confinement can further modulate the motor's binding kinetics.
Revised:  We assume that the motion of the motor is directly affected by the entropic barrier due to confinement if it is in the passive, unbound state, but not in the active, bound state . Confinement can further modulate the motor's binding kinetics.
Edit intent: clarity
Original:  We assume that the motion of the motor is directly affected by the entropic barrier due to confinement when it is in the passive, unbound state, but not in the active, bound state . Confinement can further modulate the motor's binding kinetics.
Revised:  We assume that the motion of the motor is directly affected by the entropic barrier due to confinement when it is in the passive, unbound state, but not in the active, bound state where it moves with a constant bound velocity.
Edit intent: meaning-changed
Original:  We construct a lattice model based on a Fokker Planck description of the two-state system, and study it using a kinetic Monte Carlo method . We compute transport properties such as the average velocity and the effective diffusivity of the MCC.
Revised:  We construct a lattice model based on a Fokker Planck description of the two-state system, and study it using a kinetic Monte Carlo method and compare our numerical results with analytical expressions for a mean field limit. We find that the effect of confinement strongly depends on the bound velocity and the effective diffusivity of the MCC.
Edit intent: meaning-changed
Original:  For constant binding and unbinding rates, we find that introducing confinement effectively enhances the unbinding rate and thereby reduces the motor processivity, leading to smaller effective diffusivity and average velocity . For spatially varying binding rates that depend on confinement, the average velocity is further reduced when the average binding rate is equal to the constant binding rate without confinement. However, confinement may lead to an enhancement in the average velocity if it results in a greater average binding rate than in the absence of confinement .
Revised:  For constant binding and unbinding rates, we find that introducing confinement effectively enhances the unbinding rate and thereby reduces the motor processivity, leading to smaller effective diffusivity and average velocity , except when it results in a greater average binding rate than in the absence of confinement .
Edit intent: coherence
Original:  Since (n,k) fork-join queues are prevalent in modern popular distributed systems such as Cassandra, MapReduce and Spark, estimating the sojourn time of such queues is critical for these systems' performance measurement and resource plan  .
Revised:  Since (n,k) fork-join queues are prevalent in modern popular distributed systems such as Cassandra, MapReduce and Spark, estimating the sojourn time of such queues is critical for the performance measurement and resource plan .
Edit intent: clarity
Original:  Since (n,k) fork-join queues are prevalent in modern popular distributed systems such as Cassandra, MapReduce and Spark, estimating the sojourn time of such queues is critical for these systems' performance measurement and resource plan  .
Revised:  Since (n,k) fork-join queues are prevalent in modern popular distributed systems such as Cassandra, MapReduce and Spark, estimating the sojourn time of such queues is critical for these systems' performance measurement and resource plan of these systems .
Edit intent: clarity
Original:  This brand-new technique is then used to transform the sojourn time distribution of non-purging (n,k) fork-join queues to a linear combination of the sojourn time distributions of basic (k,k)\sim (n,n) fork-join queues.
Revised:  This brand-new technique is then used to transform the sojourn time of non-purging (n,k) fork-join queues to a linear combination of the sojourn time distributions of basic (k,k)\sim (n,n) fork-join queues.
Edit intent: fluency
Original:  This brand-new technique is then used to transform the sojourn time distribution of non-purging (n,k) fork-join queues to a linear combination of the sojourn time distributions of basic (k,k)\sim (n,n) fork-join queues.
Revised:  This brand-new technique is then used to transform the sojourn time distribution of non-purging (n,k) fork-join queues into a linear combination of the sojourn time distributions of basic (k,k)\sim (n,n) fork-join queues.
Edit intent: fluency
Original:  This brand-new technique is then used to transform the sojourn time distribution of non-purging (n,k) fork-join queues to a linear combination of the sojourn time distributions of basic (k,k)\sim (n,n) fork-join queues.
Revised:  This brand-new technique is then used to transform the sojourn time distribution of non-purging (n,k) fork-join queues to a linear combination of the sojourn times of basic (k,k)\sim (n,n) fork-join queues.
Edit intent: clarity
Original:  Consequently, the expected sojourn time of non-purging (n,k) fork-join queues can be approximated with the help of existing approximations for basic fork-join queues.
Revised:  Consequently, existing approximations for basic fork-join queues can be bridged to the approximations for non-purging (n,k) fork-join queues can be approximated with the help of existing approximations for basic fork-join queues.
Edit intent: clarity
Original:  Consequently, the expected sojourn time of non-purging (n,k) fork-join queues can be approximated with the help of existing approximations for basic fork-join queues. Then, approximations for non-purging queues are used to improve the upper bounds for purging (n,k) fork-join queues.
Revised:  Consequently, the expected sojourn time of non-purging (n,k) fork-join queues . The uncovered approximations are then used to improve the upper bounds for purging (n,k) fork-join queues.
Edit intent: coherence
Original:  This brand-new technique is then used to transform the sojourn time of non-purging (n, k) fork-join queues into a linear combination of the sojourn times of basic (k, k) \sim (n, n) fork-join queues.
Revised:  This brand-new technique is then used to transform the sojourn time of non-purging (n, k) fork-join queues into a linear combination of the sojourn times of basic (k, k) ~ (n, n) fork-join queues.
Edit intent: meaning-changed
Original:  Since (n, k) fork-join queues are prevalent in modern popular distributed systems such as Cassandra, MapReduce and Spark ,  estimating the sojourn time of such queues is  critical for the performance measurement and resource plan of these systems .
Revised:  Since (n, k) fork-join queues are prevalent in popular distributed systems such as Cassandra, MapReduce and Spark , estimating the sojourn time of such queues is critical for the performance measurement and resource plan of these systems .
Edit intent: clarity
Original:  Since (n, k) fork-join queues are prevalent in modern popular distributed systems such as Cassandra, MapReduce and Spark ,  estimating the sojourn time of such queues is  critical for the performance measurement and resource plan of these systems .
Revised:  Since (n, k) fork-join queues are prevalent in modern popular distributed systems , estimating the sojourn time of such queues is critical for the performance measurement and resource plan of these systems .
Edit intent: clarity
Original:  Since (n, k) fork-join queues are prevalent in modern popular distributed systems such as Cassandra, MapReduce and Spark ,  estimating the sojourn time of such queues is  critical for the performance measurement and resource plan of these systems .
Revised:  Since (n, k) fork-join queues are prevalent in modern popular distributed systems such as Cassandra, MapReduce and Spark , erasure coding based cloud storages, and modern network protocols like multipath routing, estimating the sojourn time of such queues is critical for the performance measurement and resource plan of these systems .
Edit intent: meaning-changed
Original:  Since (n, k) fork-join queues are prevalent in modern popular distributed systems such as Cassandra, MapReduce and Spark ,  estimating the sojourn time of such queues is  critical for the performance measurement and resource plan of these systems .
Revised:  Since (n, k) fork-join queues are prevalent in modern popular distributed systems such as Cassandra, MapReduce and Spark , estimating the sojourn time of such queues is thus critical for the performance measurement and resource plan of these systems .
Edit intent: coherence
Original:  Since (n, k) fork-join queues are prevalent in modern popular distributed systems such as Cassandra, MapReduce and Spark ,  estimating the sojourn time of such queues is  critical for the performance measurement and resource plan of these systems .
Revised:  Since (n, k) fork-join queues are prevalent in modern popular distributed systems such as Cassandra, MapReduce and Spark , estimating the sojourn time of such queues is critical for the performance measurement and resource plan of computer clusters .
Edit intent: clarity
Original:  This brand-new technique is then used to transform the sojourn time of non-purging (n, k) fork-join queues into a linear combination of the sojourn times of basic (k, k) ~ (n, n) fork-join queues.
Revised:  This brand-new technique is then used to transform the sojourn time of non-purging (n, k) fork-join queues into a linear combination of the sojourn times of basic (k, k) , (k+1, k+1), ..., (n, n) fork-join queues.
Edit intent: meaning-changed
Original:  Our approach reduces the variance of the estimator by exploiting the positive correlation of these processes and improves the performance by skipping the propensity updates. Furthermore, by using propensity bounds to couple processes, our approach allows simultaneous perturbation of many reaction rates in computing the sensitivities, which further improves the efficiency of the estimator.
Revised:  For each simulation step, the nominal and perturbed processes under our coupling strategy are synchronized and often jump together, increasing their positive correlation and hence reducing the variance of the estimator. The distinctive feature of our approach in comparison with existing coupling approaches is that it only needs to maintain a single data structure storing propensity bounds of reactions during the simulation of the nominal and perturbed processes. Our approach allows to computing sensitivities of many reaction rates in computing the sensitivities, which further improves the efficiency of the estimator.
Edit intent: clarity
Original:  Furthermore, by using propensity bounds to couple processes, our approach allows simultaneous perturbation of many reaction rates in computing the sensitivities, which further improves the efficiency of the estimator.
Revised:  Furthermore, by using propensity bounds to couple processes, our approach allows simultaneous perturbation of many reaction rates simultaneously. Moreover, the data structure does not require to be updated frequently, hence improving the computational cost. This feature is especially useful when applied to large reaction networks.
Edit intent: meaning-changed
Original:  In this work, we develop the multi-level method in two directions: (1) to increase the robustness, reliability and performance of the multi-level method, we suggest an improved variance reduction method for generating the sample paths of each ensemble;
Revised:  In this work, we develop the multi-level method in two directions: (1) to increase the robustness, reliability and performance of the multi-level method, we implement an improved variance reduction method for generating the sample paths of each ensemble;
Edit intent: clarity
Original:  Counterexamples are found in models of molecular motors, of circadian cycles and of sensory adaptation. There, performances or efficiencies are not always monotonously increasing with the dissipated power. The simple general reason is that nondissipative and time-symmetric kinetic aspects are also relevant for establishing optimal functioning.
Revised:  The simple reason is that nondissipative and time-symmetric kinetic aspects are also relevant for establishing optimal functioning.
Edit intent: coherence
Original:  In fact those aspects are even crucial in the nonlinear regimes around equilibrium where we find biological processing on mesoscopic scales  .
Revised:  In fact those aspects are even crucial in the nonlinear regimes around equilibrium where we find biological processing on mesoscopic scales . We make these claims specific via examples of molecular motors, of circadian cycles and of sensory adaptation, whose performance in some regimes is indeed spoiled by increasing the dissipated power. We use the relation between dissipation and the amount of time-reversal breaking to keep the discussion quantitative also in effective models where the physical entropy production is not clearly identifiable .
Edit intent: meaning-changed
Original:  Based on experimental observations, we design an adaptive technique that aims at setting the best combination of thread-level parallelism and CPU-core power state depending on the workload profile of the multi-threaded application.
Revised:  Based on experimental observations, we design an adaptive technique that selects in linear time the optimal combination of thread-level parallelism and CPU-core power state depending on the workload profile of the multi-threaded application.
Edit intent: meaning-changed
Original:  Based on experimental observations, we design an adaptive technique that aims at setting the best combination of thread-level parallelism and CPU-core power state depending on the workload profile of the multi-threaded application.
Revised:  Based on experimental observations, we design an adaptive technique that aims at setting the best combination of thread-level parallelism and CPU-core power state for the specific workload profile of the multi-threaded application.
Edit intent: clarity
Original:  We develop results that guarantee the existence of a solution , indicate properties that our risk measure fulfills, and characterize the resulting minimum cost as a deviation measure. We generalize this approach to a robust framework, where the minimization is over a supremum of expectations, based on a convex set of probability measures .
Revised:  We develop results that guarantee the existence of a solution and explore the properties of minimizer and minimum as risk and deviation measures, respectively .
Edit intent: clarity
Original:  We relate this robust approach with the dual representation of coherent risk measures. Moreover, we suggest the use of our loss function in the verification of risk estimation or forecasting quality. Two empirical illustrations are carried out to demonstrate the use of our approach in the capital determinationand selection of risk prediction models.
Revised:  Empirical illustration is carried out to demonstrate the use of our approach in the capital determinationand selection of risk prediction models.
Edit intent: coherence
Original:  The nearest site Voronoi diagram (NVD) and the farthest site Voronoi diagram (FVD) are the particular cases of k=1 and k=n-1, respectively.
Revised:  The (nearest site) Voronoi diagram (NVD) and the farthest site Voronoi diagram (FVD) are the particular cases of k=1 and k=n-1, respectively.
Edit intent: fluency
Original:  Moreover, NVD (P) and FVD (P ) can be computed in O(n\log n) time using O(n) space [Preparata, Shamos, Springer'85].
Revised:  Moreover, NVD and FVD for P can be computed in O(n\log n) time using O(n) space [Preparata, Shamos, Springer'85].
Edit intent: clarity
Original:  \ compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O%DIFDELCMD < \bigl(%%%  n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K) %DIFDELCMD < \bigr)%%%  . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O (( \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).
Revised:  , we compute the family of all higher-order Voronoi diagrams of order k=1,\dots,K for P in total time O%DIFDELCMD < \bigl(%%% n^2 K^5{s}(\log s+ )) or in total deterministic time O(n^2 K^5{s}(\log s+} K\log K) %DIFDELCMD < \bigr)%%% . Previously, for Voronoi diagrams, the only known s-workspace algorithm runs in expected time O (( \bigl( n^2/s)\log s+n\log s\log^* s) [Korman et al., WADS'15] and only works for NVD (P) (i.e., k=1).
Edit intent: fluency