wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We present an algorithm of O( (n + m) log(n + m )) time for any m . These problems may have applications in mobile sensor barrier coverage in wireless sensor networks.
Revised:  We present an algorithm of O( (n + m) log(n + m \log m+n\log m \log n) time for any m . These problems may have applications in mobile sensor barrier coverage in wireless sensor networks.
Edit intent: meaning-changed
Original:  As a result, we compare 21 popular measures and show important differences in their behavior. and IBA_\alpha(G-mean), we analytically derive parameter thresholds that change measure properties.
Revised:  As a result, we compare 22 popular measures and show important differences in their behavior. and IBA_\alpha(G-mean), we analytically derive parameter thresholds that change measure properties.
Edit intent: meaning-changed
Original:  As a result, we compare 21 popular measures and show important differences in their behavior. and IBA_\alpha(G-mean), we analytically derive parameter thresholds that change measure properties.
Revised:  As a result, we compare 21 popular measures and show important differences in their behaviour. Moreover, for parametric measures such as the F_{\beta and IBA_\alpha(G-mean), we analytically derive parameter thresholds that change measure properties.
Edit intent: meaning-changed
Original: A pseudocircle is a simple closed curve on some surface . Arrangements of pseudocircles were introduced by Gr\"unbaum, who defined them as collections of pseudocircles that pairwise intersect in exactly two points, at which they cross.
Revised: A pseudocircle is a simple closed curve on some surface ; an arrangement of pseudocircles is a collection of pseudocircles that pairwise intersect in exactly two points, at which they cross.
Edit intent: clarity
Original:  There are several variations on this notion in the literature, one of which requires that no three pseudocircles have a point in common. Working under this definition, Ortner proved that an arrangement of pseudocircles is embeddable into the sphere if and only if all of its subarrangements of size at most 4 are embeddable into the sphere .
Revised:  Ortner proved that an arrangement of pseudocircles is embeddable into the sphere if and only if all of its subarrangements of size at most 4 are embeddable into the sphere .
Edit intent: clarity
Original:  Working under this definition, Ortner proved that an arrangement of pseudocircles is embeddable into the sphere if and only if all of its subarrangements of size at most 4 are embeddable into the sphere .
Revised:  Working under this definition, Ortner proved that an arrangement of pseudocircles is embeddable into the sphere if and only if all of its subarrangements of size at most four are embeddable into the sphere .
Edit intent: fluency
Original:  Working under this definition, Ortner proved that an arrangement of pseudocircles is embeddable into the sphere if and only if all of its subarrangements of size at most 4 are embeddable into the sphere . Ortner asked if an analogous result held for embeddability into a compact orientable surface \Sigma_g of genus g>0.
Revised:  Working under this definition, Ortner proved that an arrangement of pseudocircles is embeddable into the sphere if and only if all of its subarrangements of size at most 4 are embeddable into the sphere , and asked if an analogous result held for embeddability into a compact orientable surface \Sigma_g of genus g>0.
Edit intent: coherence
Original:  Ortner asked if an analogous result held for embeddability into a compact orientable surface \Sigma_g of genus g>0. In this paper we answer this question , under an even more general definition of an arrangement, in which the pseudocircles in the collection are not required to intersect each other, or that the intersections are crossings: it suffices to have one pseudocircle that intersects all other pseudocircles in the collection.
Revised:  Ortner asked if an analogous result held for embeddability into orientable surfaces of higher genus. We answer this question , under an even more general definition of an arrangement, in which the pseudocircles in the collection are not required to intersect each other, or that the intersections are crossings: it suffices to have one pseudocircle that intersects all other pseudocircles in the collection.
Edit intent: clarity
Original:  In this paper we answer this question , under an even more general definition of an arrangement, in which the pseudocircles in the collection are not required to intersect each other, or that the intersections are crossings: it suffices to have one pseudocircle that intersects all other pseudocircles in the collection. We show that under this more general notion, an arrangement of pseudocircles is embeddable into \Sigma_g if and only if all of its subarrangements of size at most 4g+ 5 areembeddable into \Sigma_g, and that this can be improved to 4g+4 under the concept of an arrangement used by Ortner.
Revised:  In this paper we answer this question positively: An arrangement of pseudocircles is embeddable into \Sigma_g if and only if all of its subarrangements of size at most 4g+ 5 areembeddable into \Sigma_g, and that this can be improved to 4g+4 under the concept of an arrangement used by Ortner.
Edit intent: clarity
Original:  We show that under this more general notion, an arrangement of pseudocircles is embeddable into \Sigma_g if and only if all of its subarrangements of size at most 4g+ 5 areembeddable into \Sigma_g, and that this can be improved to 4g+4 under the concept of an arrangement used by Ortner.
Revised:  We show that under this more general notion, an arrangement of pseudocircles is embeddable into an orientable surface of genus~g if and only if all of its subarrangements of size at most 4g+ 5 areembeddable into \Sigma_g, and that this can be improved to 4g+4 under the concept of an arrangement used by Ortner.
Edit intent: meaning-changed
Original:  We show that under this more general notion, an arrangement of pseudocircles is embeddable into \Sigma_g if and only if all of its subarrangements of size at most 4g+ 5 areembeddable into \Sigma_g, and that this can be improved to 4g+4 under the concept of an arrangement used by Ortner. Our framework also allows us to generalize this result to arrangements of other objects, such as arcs\emph{ .
Revised:  We show that under this more general notion, an arrangement of pseudocircles is embeddable into \Sigma_g if and only if all of its subarrangements of size at most 4g+ 4 are. Moreover, this bound is tight. We actually have similar results for a much general notion of arrangement, which we call an\emph{ .
Edit intent: meaning-changed
Original: This note proposes a consistent bootstrap-based distributional approximation for cube root consistent estimators such as the maximum score estimator of Manski (1975)and the isotonic density estimator of Grenander (1956).
Revised: This paper proposes a consistent bootstrap-based distributional approximation for cube root consistent estimators such as the maximum score estimator of Manski (1975)and the isotonic density estimator of Grenander (1956).
Edit intent: clarity
Original: This note proposes a consistent bootstrap-based distributional approximation for cube root consistent estimators such as the maximum score estimator of Manski (1975)and the isotonic density estimator of Grenander (1956). In both cases , the standard nonparametric bootstrap is known to be inconsistent.
Revised: This note proposes a consistent bootstrap-based distributional approximation for cube root consistent and related estimators exhibiting a Chernoff (1964)-type limiting distribution. For estimators of this kind , the standard nonparametric bootstrap is known to be inconsistent.
Edit intent: meaning-changed
Original:  This modification leads to a generic and easy-to-implement resampling method for inference that is conceptually distinct from other available distributional approximations based on some form of modified bootstrap. We offer simulation evidence showcasing the performance of our inference method in finite samples. An extension of our methodology to general M-estimation problems is also discussed .
Revised:  This modification leads to a generic and easy-to-implement resampling method for inference that is conceptually distinct from other available distributional approximations . We illustrate the applicability of our core idea with six canonical examples in statistics, machine learning, econometrics, and biostatistics. Simulation evidence is also provided .
Edit intent: meaning-changed
Original:  Otherwise, our algorithm outputs the visibility polygon corresponding to the exterior visibility of p. * An  output-sensitive algorithm to compute the weak visibility polygon corresponding to any query line segment located interior to the simple polygon amid both the vertex insertions and deletions to the simple polygon.
Revised:  Otherwise, our algorithm outputs the visibility polygon corresponding to the exterior visibility of p. * An incremental algorithm to maintain the weak visibility polygon of a fixed-line segment located interior to the simple polygon amid vertex insertions to the simple polygon. The time complexity to update the weak visibility polygon of a line segment pq due to the insertion of vertex v to the current simple polygon is expressed in terms of the sum of the number of combinatorial updates needed to the geodesic shortest path trees rooted at p and q due to the insertion of v. * An output-sensitive algorithm to compute the weak visibility polygon corresponding to any query line segment located interior to the simple polygon amid both the vertex insertions and deletions to the simple polygon.
Edit intent: meaning-changed
Original:  The results enable a correct and easy-to-implement modularization of capital requirements into a market risk and a non-hedgeable risk component: the paper provides a stable expression for the financial benchmark against which the company's asset allocation must be measured to obtain the market risk component.
Revised:  The results enable a correct and easy-to-implement modularization of capital requirements into a market risk and a non-hedgeable risk component.
Edit intent: coherence
Original:  This can be accomplished by taking various routes through some auxiliary considerations, namely Arrow-Debreu securities, digital options or backward processes when the CRR model is extended to an infinite state space . The latter also leads to an interesting new phenomenon  .
Revised:  This can be accomplished by taking various routes through some auxiliary considerations, namely Arrow-Debreu securities, digital options or backward processes when the CRR model is extended to an infinite state space which leads to an interesting new phenomenon .
Edit intent: clarity
Original: The Meeting problem for k\geq 2 searchers in a polygon P (possibly with holes) consists in making the searchers move within P, according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions.
Revised: The Meeting problem for k\geq 2 searchers in a polygon P (possibly with holes) consists in making the searchers move within P, according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions.
Edit intent: fluency
Original:  The algorithms are self-stabilizing even in such a memoryless model, in the sense that the searchers may be located anywhere in the polygon when the execution begins, and hence the information they initially encode is arbitrary  .
Revised:  The algorithms are self-stabilizing even in such a memoryless model, in the sense that the searchers may be located anywhere in the polygon when the execution begins, and hence the information they initially encode is arbitrary . Our algorithms use a self-stabilizing map construction subroutine which is of independent interest .
Edit intent: meaning-changed
Original:  The notion of effective scaling domain is introduced and its properties are discussed .
Revised:  It is then pointed out that such a relationship opens a door to a decomposition scheme, called progressive hedging, for solving multistage risk minimization and regret minimization problems. In particular, the classical progressive hedging algorithm is modified in order to handle a new class of constraints that arises from a reformulation of risk and regret minimization problems. Numerical results are provided to show the efficiency of the progressive hedging algorithms .
Edit intent: meaning-changed
Original: We prove that the variance swap rate  equals the price of a co-terminal European-style contract when the underlying is an exponential Markov process, time-changed by an arbitrary continuous stochastic clock, which has arbitrary correlation with the driving Markov process .
Revised: We prove that the variance swap rate (fair strike) equals the price of a co-terminal European-style contract when the underlying is an exponential Markov process, time-changed by an arbitrary continuous stochastic clock, which has arbitrary correlation with the driving Markov process .
Edit intent: meaning-changed
Original: We prove that the variance swap rate  equals the price of a co-terminal European-style contract when the underlying is an exponential Markov process, time-changed by an arbitrary continuous stochastic clock, which has arbitrary correlation with the driving Markov process . The payoff function G of the European contract that prices the variance swap satisfies an ordinary integro-differential equation, which depends only on the dynamics of the Markov process, not on the clock.
Revised: We prove that the variance swap rate equals the price of a co-terminal European-style contract when the underlying is an exponential Markov process, time-changed by an arbitrary continuous stochastic clock, which has arbitrary correlation with the driving Markov process , provided that the payoff function G of the European contract that prices the variance swap satisfies an ordinary integro-differential equation, which depends only on the dynamics of the Markov process, not on the clock.
Edit intent: clarity
Original: We develop a uniform asymptotic expansion for the empirical distribution function of residuals in the nonparametric IV regression. Such expansion opens a door forconstruction of a broad range of residual-based specification tests in nonparametric IV models. Building on obtained result, we develop a  test for the separability of unobservables in econometric models with endogeneity .
Revised: It is common to assume in the empirical practice that the observables are additively separable from the unobservables, especially, when the former are endogenous. This is done because it is widely recognized that identification and estimation challenges arise when interactions between the two are allowed for. Starting from the nonseparable IV model, where the IV is independent of the unobservable, we develop a test for the separability of unobservables in econometric models with endogeneity .
Edit intent: meaning-changed
Original:  The test is based on verifying the independence condition between residuals of the NPIV estimator and the instrument and can distinguish between the non-separable and the separable specification under endogeneity .
Revised:  The test relies on the estimation of the separable IV model and the verification of the independence restriction between the residual and the instrumental variable imposed by the non-separable model. To obtain a large-sample approximation to the test statistics, we develop a novel uniform asymptotic expansion of the empirical distribution function of residuals that lead to a Donsker-type central limit theorem. Using a dataset drawn from the 2015 US Consumer Expenditure Survey, we find that the test rejects the separability in Engel curves for most of the commodities .
Edit intent: meaning-changed
Original:  The test relies on the estimation of the separable IV model and the verification of the independence restriction between the residual and the instrumental variable imposed by the non-separable model. To obtain a large-sample approximation to the test statistics , we develop a novel uniform asymptotic expansion of the empirical distribution function of residuals that lead to a Donsker-type central limit theorem .
Revised:  The large-sample approximation to the test statistics , we develop a novel uniform asymptotic expansion of the empirical distribution function of residuals that lead to a Donsker-type central limit theorem .
Edit intent: coherence
Original:  To obtain a large-sample approximation to the test statistics , we develop a novel uniform asymptotic expansion of the empirical distribution function of residuals that lead to a Donsker-type central limit theorem .
Revised:  To obtain a large-sample distribution of the test statistics is nonstandard and relies on a novel Donsker-type central limit theorem for the empirical distribution function of residuals that lead to a Donsker-type central limit theorem .
Edit intent: clarity
Original: The choice between deterministic and stochastic modeling can lead to dramatically different theoretical conclusions regarding the steady state behavior of a gene regulatory network (GRN). This is particularly interesting when low-molecular counts and slow TF-gene binding /unbinding lead to the emergence of new phenotypes in the stochastic model that are not reflected in the corresponding deterministic model. This work uncovers a mechanism that underlies this emergence of multiple modes under slow slow promoter kinetics, and studies it theoretically.
Revised: Phenotypical variability in the absence of genetic variation often reflects complex energetic landscapes associated with underlying gene regulatory networks (GRNs). In this view, different phenotypes are associated with alternative states of complex nonlinear systems: stable attractors in deterministic models or modes of stationary distributions in stochastic descriptions. We provide theoretical and practical characterizations of these landscapes, specifically focusing on stochastic slow promoter kinetics, a time scale relevant when transcription factor binding and unbinding are affected by epigenetic processes like DNA methylation and chromatin remodeling. In this case, largely unexplored except for numerical simulations, adiabatic approximations of promoter kinetics are not appropriate. In contrast to the existing literature, we provide rigorous analytic characterizations of multiple modes under slow slow promoter kinetics, and studies it theoretically.
Edit intent: meaning-changed
Original:  This work uncovers a mechanism that underlies this emergence of multiple modes under slow slow promoter kinetics, and studies it theoretically. Mathematical tools from singular perturbation theory are employed in order to analytically characterize stationary distributions of Chemical Master Equations for GRN's, in the limit of slow switching, as a mixture of Poisson distributions This approach, which may be interpreted as a finite-dimensional reduction of a countable Markov chain, offers a rigorous framework to explain phenomena such as non-genetic population heterogeneity and transcriptional bursting .
Revised:  This work uncovers a mechanism that underlies this emergence of multiple modes . A general formal approach gives insight into the influence of parameters and the prediction of how changes in GRN wiring, for example through mutations or artificial interventions, impact the possible number, location, and likelihood of alternative states. We adapt tools from the mathematical field of singular perturbation theory are employed in order to analytically characterize stationary distributions of Chemical Master Equations for GRN's, in the limit of slow switching, as a mixture of Poisson distributions This approach, which may be interpreted as a finite-dimensional reduction of a countable Markov chain, offers a rigorous framework to explain phenomena such as non-genetic population heterogeneity and transcriptional bursting .
Edit intent: coherence
Original:  Mathematical tools from singular perturbation theory are employed in order to analytically characterize stationary distributions of Chemical Master Equations for GRN's, in the limit of slow switching, as a mixture of Poisson distributions This approach, which may be interpreted as a finite-dimensional reduction of a countable Markov chain, offers a rigorous framework to explain phenomena such as non-genetic population heterogeneity and transcriptional bursting .
Revised:  Mathematical tools from singular perturbation theory to represent stationary distributions of Chemical Master Equations for GRN's, in the limit of slow switching, as a mixture of Poisson distributions This approach, which may be interpreted as a finite-dimensional reduction of a countable Markov chain, offers a rigorous framework to explain phenomena such as non-genetic population heterogeneity and transcriptional bursting .
Edit intent: clarity
Original:  Mathematical tools from singular perturbation theory are employed in order to analytically characterize stationary distributions of Chemical Master Equations for GRN's, in the limit of slow switching, as a mixture of Poisson distributions This approach, which may be interpreted as a finite-dimensional reduction of a countable Markov chain, offers a rigorous framework to explain phenomena such as non-genetic population heterogeneity and transcriptional bursting .
Revised:  Mathematical tools from singular perturbation theory are employed in order to analytically characterize stationary distributions of Chemical Master Equations for GRNs as mixtures of Poisson distributions This approach, which may be interpreted as a finite-dimensional reduction of a countable Markov chain, offers a rigorous framework to explain phenomena such as non-genetic population heterogeneity and transcriptional bursting .
Edit intent: clarity
Original:  Mathematical tools from singular perturbation theory are employed in order to analytically characterize stationary distributions of Chemical Master Equations for GRN's, in the limit of slow switching, as a mixture of Poisson distributions This approach, which may be interpreted as a finite-dimensional reduction of a countable Markov chain, offers a rigorous framework to explain phenomena such as non-genetic population heterogeneity and transcriptional bursting .
Revised:  Mathematical tools from singular perturbation theory are employed in order to analytically characterize stationary distributions of Chemical Master Equations for GRN's, in the limit of slow switching, as a mixture of Poisson distributions and obtain explicit formulas for the locations and probabilities of metastable states as a function of the parameters describing the system .
Edit intent: clarity
Original:  As illustrations, the theory is used in order to tease out the role of cooperative binding in stochastic models in comparison to deterministic models, and applications are given to various model systems, including isolated or populations of toggle switches and a trans-differentiation network.
Revised:  As illustrations, the theory is used to tease out the role of cooperative binding in stochastic models in comparison to deterministic models, and applications are given to various model systems, including isolated or populations of toggle switches and a trans-differentiation network.
Edit intent: coherence
Original:  As illustrations, the theory is used in order to tease out the role of cooperative binding in stochastic models in comparison to deterministic models, and applications are given to various model systems, including isolated or populations of toggle switches and a trans-differentiation network.
Revised:  As illustrations, the theory is used in order to tease out the role of cooperative binding in stochastic models in comparison to deterministic models, and applications are given to various model systems, such as toggle switches in isolation or in communicating populations, a synthetic oscillator and a trans-differentiation network.
Edit intent: meaning-changed