wanyu/IteraTeR_full_sent huggingface dataset:
Original: We show that a law-invariant pricing functional defined on a general Orlicz space is typically incompatible with frictionless risky assets in the sense that one and only one of the following alternatives can hold: Either every risky payoff has a strictly-positive bid-ask spread or the pricing functional is given by an expectation and, hence, every payoff has zero bid-ask spread. In doing so we extend and unify a variety of "collapse to the mean" results from the literature and highlight the key role played by law invariance in causing the collapse.
Revised: We show that a law-invariant functionals. Our results extend well-known results from the literature and highlight the key role played by law invariance in causing the collapse.
Edit intent: clarity
Original:  In doing so we extend and unify a variety of "collapse to the mean" results from the literature and highlight the key role played by law invariance in causing the collapse.As a byproduct, we derive a number of applications to law-invariant acceptance sets and risk measures as well as Schur-convex functionals .
Revised:  In doing so we extend and unify a variety of "collapse to the mean" results from the literature to a large class of spaces of random variables. We sometimes obtain sharper versions, even for the well-studied case of bounded random variables. Our approach builds on two fundamental structural results for law-invariant acceptance sets and risk measures as well as Schur-convex functionals .
Edit intent: meaning-changed
Original: As a byproduct, we derive a number of applications to law-invariant acceptance sets and risk measures as well as Schur-convex functionals .
Revised: As a byproduct, we derive a number of applications to law-invariant functionals: the equivalence of law invariance and Schur convexity, i.e., monotonicity with respect to the convex stochastic order, and the fact that a law-invariant functional is fully determined by its behaviour on bounded random variables. We show how to apply these results to provide a unifying perspective on the literature on law-invariant functionals, with special emphasis on quantile-based representations, including Kusuoka representations, dilatation monotonicity, and infimal convolutions .
Edit intent: meaning-changed
Original:  Here we present a fully-automated method of flagellum identification from videomicroscopy based on the fact that the flagella appear to be of approximately constant width when viewed with typical optics. This approximate morphological characteristic, inherent in the ultrastructure of URLanelle, is conserved across many eukaryotes.
Revised:  Here we present a fully-automated method of flagellum identification from videomicroscopy based on the fact that the flagella appear to be of approximately constant width when viewed by microscopy.
Edit intent: clarity
Original:  We demonstrate the effectiveness of the algorithm by application to captured videomicroscopy of Leishmania mexicana, a parasitic monoflagellate of the family Trypanosomatidae and the cause of a major but neglected human disease, leishmaniasis. Both high accuracy and remarkable throughput are achieved via this unsupervised method, obtaining results comparable in quality to previous studies of closely-related species but achieved without the need for precursory measurements or the development of a specialised heuristic .
Revised:  We demonstrate the effectiveness of the algorithm by application to captured videomicroscopy of Leishmania mexicana, a parasitic monoflagellate of the family Trypanosomatidae . ImageJ Macros for flagellar identification are provided, and high accuracy and remarkable throughput are achieved via this unsupervised method, obtaining results comparable in quality to previous studies of closely-related species but achieved without the need for precursory measurements or the development of a specialised heuristic .
Edit intent: meaning-changed
Original:  Both high accuracy and remarkable throughput are achieved via this unsupervised method, obtaining results comparable in quality to previous studies of closely-related species but achieved without the need for precursory measurements or the development of a specialised heuristic . Further, we process a dataset documenting a canonical microswimmer that has accessory flagellar structures, the motile human spermatozoon, thus.. .
Revised:  Both high accuracy and remarkable throughput are achieved via this unsupervised method, obtaining results comparable in quality to previous studies of closely-related species but achieved without the need for precursory measurements or the development of a specialised heuristic , enabling in general the automated generation of digitised kinematic descriptions of flagellar beating from videomicroscopy .
Edit intent: clarity
Original: We present a routing algorithm for the Theta-4-graph  that computes a path between any two vertices s and t having length at most 17 times the Euclidean distance between s and t.
Revised: We present a routing algorithm for the directed \Theta_4-graph, here denoted as the \overrightarrow{\Theta_4 that computes a path between any two vertices s and t having length at most 17 times the Euclidean distance between s and t.
Edit intent: meaning-changed
Original: We present a routing algorithm for the Theta-4-graph  that computes a path between any two vertices s and t having length at most 17 times the Euclidean distance between s and t.
Revised: We present a routing algorithm for the Theta-4-graph -graph, that computes a path between any two vertices s and t having length at most 17 times the Euclidean distance between s and t.
Edit intent: fluency
Original:  This provides the first known online, local, competitive routing algorithm with constant routing ratio for the Theta-4-graph , as well as improving the best known upper bound on the spanning ratio of these graphs from 237 to 17.  \approx 17.03.}
Revised:  This provides the first known online, local, competitive routing algorithm with constant routing ratio for the \Theta_4-graph , as well as improving the best known upper bound on the spanning ratio of these graphs from 237 to 17. \approx 17.03.}
Edit intent: fluency
Original:  This provides the first known online, local, competitive routing algorithm with constant routing ratio for the Theta-4-graph , as well as improving the best known upper bound on the spanning ratio of these graphs from 237 to 17.  \approx 17.03.}
Revised:  This provides the first known online, local, competitive routing algorithm with constant routing ratio for the Theta-4-graph , as well as improving the best known upper bound on the spanning ratio of these graphs from 237 to 17. We also show that without this additional bit of information, the routing ratio increases to \sqrt{290 \approx 17.03.}
Edit intent: meaning-changed
Original: We propose a framework for ranking confidence interval estimators in terms of their uniform coverage accuracy. The key ingredient is the (existence and) quantification of the error in coverage of competing confidence intervals , uniformly over some empirically-relevant class of data generating processes.
Revised: In this paper we develop new confidence intervals for local polynomial regression, which minimize their worse-case coverage error and length in large samples. Our results rely on novel , uniformly over some empirically-relevant class of data generating processes.
Edit intent: meaning-changed
Original:  The key ingredient is the (existence and) quantification of the error in coverage of competing confidence intervals , uniformly over some empirically-relevant class of data generating processes. The framework employs the "check" function to quantify coverage error loss, which allows researchers to incorporate their preference in terms of over- and under-coverage, where confidence intervals attaining the best-possible uniform coverage error are minimax optimal. We demonstrate the usefulness of our framework with three distinct applications. First, we establish noveluniformly valid Edgeworth expansions for nonparametric local polynomial regression, offering some technical results that may be of independent interest, and use them to characterize the coverage error of and rank confidence interval estimatorsfor the regression function and its derivatives.
Revised:  The key ingredient is the (existence and) quantification of the error in coverage of competing confidence intervals , valid Edgeworth expansions for nonparametric local polynomial regression, offering some technical results that may be of independent interest, and use them to characterize the coverage error of and rank confidence interval estimatorsfor the regression function and its derivatives.
Edit intent: coherence
Original:  First, we establish noveluniformly valid Edgeworth expansions for nonparametric local polynomial regression, offering some technical results that may be of independent interest, and use them to characterize the coverage error of and rank confidence interval estimatorsfor the regression function and its derivatives. As a second application we consider inference in least squares linear regression under potential misspecification, ranking interval estimators utilizing uniformly valid expansions already established in the literature.
Revised:  First, we establish noveluniformly valid Edgeworth expansions for t-statistics based on local polynomial methods, which are established uniformly over relevant classes of data generating processes and interval estimators. These higher-order expansions also allow for the uniform kernel and any derivative order, significantly improving on previous technical results available in the literature.
Edit intent: clarity
Original: In this paper we develop new confidence intervals for  local polynomial regression , which minimize their worse-case coverage error and length in large samples. Our results rely on novel , valid Edgeworth expansions for t-statistics based on local polynomial methods, which are established uniformly over relevant classes of data generating processes and interval estimators .
Revised: In this paper we develop new confidence intervals for local polynomial regression . This bound depends on the smoothness of the population regression function, the smoothness exploited by the inference procedure, and on whether the evaluation point of interest is in the interior or on the boundary of the support of the regression function. Our results also cover inference on derivatives of the regression function, in which case we find that the minimax coverage error bound does not depend on the order of the derivative being estimated. We show that robust bias corrected confidence intervals are able to attain the minimax rate when coupled with the principled, inference-optimal tuning parameter selections we propose. In addition, we show how the large-sample interval length can be further optimized through choice of the kernel function and other tuning parameters. Our main theoretical results rely on novel , valid Edgeworth expansions for t-statistics based on local polynomial methods, which are established uniformly over relevant classes of data generating processes and interval estimators .
Edit intent: meaning-changed
Original:  These higher-order expansions also allow for the uniform kernel and any derivative order, significantly improving on previous technical results available in the literature . In addition, we discuss principled, inference-optimal tuning parameter (bandwidth) selection and kernel functions. The main methodological results obtained in this paper are implemented in companion%DIFDELCMD < {\sf %%% R andStata software packages .
Revised:  These higher-order expansions also allow for the uniform kernel and any derivative order, significantly improving on previous technical results available in the literature %DIFDELCMD < {\sf %%% R andStata software packages .
Edit intent: coherence
Original: We characterize the minimax bound on coverage error of Wald-type confidence intervals for nonparametric local polynomial regression . This bound depends on the smoothness of the population regression function, the smoothness exploited by the inference procedure, and on whether the evaluation point of interest is in the interior or on the boundary of the support of the regression function.
Revised: We characterize the minimax bound on coverage error of Wald-type confidence intervals for nonparametric local polynomial regression methods under random sampling. We prove Edgeworth expansions for t statistics and coverage error expansions for interval estimators that (i) hold uniformly in the data generating process, (ii) allow for the uniform kernel, and (iii) cover estimation of derivatives of the regression function. The terms of the higher-order expansions, and their associated rates as a function of the sample size and bandwidth sequence, depend on the smoothness of the population regression function, the smoothness exploited by the inference procedure, and on whether the evaluation point of interest is in the interior or on the boundary of the support of the regression function.
Edit intent: meaning-changed
Original:  This bound depends on the smoothness of the population regression function, the smoothness exploited by the inference procedure, and on whether the evaluation point of interest is in the interior or on the boundary of the support of the regression function.
Revised:  This bound depends on the smoothness of the population regression function, the smoothness exploited by the inference procedure, and on whether the evaluation point is in the interior or on the boundary of the support of the regression function.
Edit intent: clarity
Original:  This bound depends on the smoothness of the population regression function, the smoothness exploited by the inference procedure, and on whether the evaluation point of interest is in the interior or on the boundary of the support of the regression function. Our results also cover inference on derivatives of the regression function, in which case we find that the minimax coverage error bound does not depend on the order of the derivative being estimated. We show that robust bias corrected confidence intervals are able to attain the minimax rate when coupled with the principled, inference-optimal tuning parameter selections we propose.
Revised:  This bound depends on the smoothness of the population regression function, the smoothness exploited by the inference procedure, and on whether the evaluation point of interest is in the interior or on the boundary of the support . We prove that robust bias corrected confidence intervals are able to attain the minimax rate when coupled with the principled, inference-optimal tuning parameter selections we propose.
Edit intent: coherence
Original:  We show that robust bias corrected confidence intervals are able to attain the minimax rate when coupled with the principled, inference-optimal tuning parameter selections we propose. In addition, we show how the large-sample interval length can be further optimized through choice of the kernel function and other tuning parameters. Our main theoretical results rely on novel Edgeworth expansions that are proven to hold uniformly over relevant classes of data generating processes. These higher-order expansions allow for the uniform kernel and any derivative order, improving on previous technical results available in the literature   .
Revised:  We show that robust bias corrected confidence intervals are able to attain the minimax rate when coupled with the principled, inference-optimal bandwidth selectors. The main methodological results are implemented in companion .
Edit intent: clarity
Original:  Two skeletal algorithms are defined and instantiated with different separation oracles to yield a sequential convex hull algorithm, a new version of Benson's algorithm with the theoretically best possible iteration count, and the new algorithm.
Revised:  Two skeletal algorithms are defined which focus on the combinatorial part. Using different single-objective optimization problems - called oracle calls - yield different algorithms, such as a sequential convex hull algorithm, a new version of Benson's algorithm with the theoretically best possible iteration count, and the new algorithm.
Edit intent: meaning-changed
Original:  Two skeletal algorithms are defined and instantiated with different separation oracles to yield a sequential convex hull algorithm, a new version of Benson's algorithm with the theoretically best possible iteration count, and the new algorithm.
Revised:  Two skeletal algorithms are defined and instantiated with different separation oracles to yield a sequential convex hull algorithm, another version of Benson's algorithm with the theoretically best possible iteration count, and the new algorithm.
Edit intent: clarity
Original:  Two skeletal algorithms are defined and instantiated with different separation oracles to yield a sequential convex hull algorithm, a new version of Benson's algorithm with the theoretically best possible iteration count, and the new algorithm.
Revised:  Two skeletal algorithms are defined and instantiated with different separation oracles to yield a sequential convex hull algorithm, a new version of Benson's algorithm with the theoretically best possible iteration count, the dual algorithm of Ehrgott, L\"ohne and Shao, and the new algorithm.
Edit intent: meaning-changed
Original:  The method is based on novel results for  smooth and discrete Hodge-Morrey-Friedrichs decomposition on manifolds with boundary and subdivides the WSS vector field into the five components: gradient (curl-free), co-gradient (divergence-free), and three harmonic fields induced from the boundary : center, Neumann and Dirichlet  .
Revised:  The method is based on novel results for the smooth and discrete Hodge-Morrey-Friedrichs decomposition on manifolds with boundary and subdivides the WSS vector field into the five components: gradient (curl-free), co-gradient (divergence-free), and three harmonic fields induced from the boundary : center, Neumann and Dirichlet .
Edit intent: fluency
Original:  The method is based on novel results for  smooth and discrete Hodge-Morrey-Friedrichs decomposition on manifolds with boundary and subdivides the WSS vector field into the five components: gradient (curl-free), co-gradient (divergence-free), and three harmonic fields induced from the boundary : center, Neumann and Dirichlet  .
Revised:  The method is based on novel results for smooth and discrete Hodge-Morrey-Friedrichs decomposition on manifolds with boundary and subdivides the WSS vector field into five components: gradient (curl-free), co-gradient (divergence-free), and three harmonic fields induced from the boundary : center, Neumann and Dirichlet .
Edit intent: fluency
Original:  The method is based on novel results for  smooth and discrete Hodge-Morrey-Friedrichs decomposition on manifolds with boundary and subdivides the WSS vector field into the five components: gradient (curl-free), co-gradient (divergence-free), and three harmonic fields induced from the boundary : center, Neumann and Dirichlet  .
Revised:  The method is based on novel results for smooth and discrete Hodge-Morrey-Friedrichs decomposition on manifolds with boundary and subdivides the WSS vector field into the five components: gradient (curl-free), co-gradient (divergence-free), and three harmonic fields induced from the boundary , which are called the center, Neumann and Dirichlet .
Edit intent: coherence
Original:  The method is based on novel results for  smooth and discrete Hodge-Morrey-Friedrichs decomposition on manifolds with boundary and subdivides the WSS vector field into the five components: gradient (curl-free), co-gradient (divergence-free), and three harmonic fields induced from the boundary : center, Neumann and Dirichlet  .
Revised:  The method is based on novel results for smooth and discrete Hodge-Morrey-Friedrichs decomposition on manifolds with boundary and subdivides the WSS vector field into the five components: gradient (curl-free), co-gradient (divergence-free), and three harmonic fields induced from the boundary : center, Neumann and Dirichlet fields .
Edit intent: clarity
Original: We consider a connection-level model proposed by Massouli\'{e} and Roberts for bandwidth sharing among file transfer flows in a communication network , and we study weighted proportionally fair sharing policies where the weights represent the relative importance of flows on different routes.
Revised: We consider a connection-level model proposed by Massouli\'{e} and Roberts for bandwidth sharing among file transfer flows in a communication network . We study weighted proportionally fair sharing policies where the weights represent the relative importance of flows on different routes.
Edit intent: coherence
Original: We consider a connection-level model proposed by Massouli\'{e} and Roberts for bandwidth sharing among file transfer flows in a communication network , and we study weighted proportionally fair sharing policies where the weights represent the relative importance of flows on different routes. We are interested in characterizing performance in the heavy-traffic regime. Existing work on this problem has focused on diffusion approximations, which were first studied by Kang et al. (2009). However, except for the case where the weights of all the routes are equal, the steady-state distribution of the limiting diffusion process is unknown and thus there are no explicit-form characterizations, even when exponential file size distributions are assumed.
Revised: We consider a connection-level model proposed by Massouli\'{e} and Roberts for bandwidth sharing among file transfer flows in a communication network , and we study weighted proportionally fair sharing policies and establish explicit-form characterizations, even when exponential file size distributions are assumed.
Edit intent: coherence
Original:  However, except for the case where the weights of all the routes are equal, the steady-state distribution of the limiting diffusion process is unknown and thus there are no explicit-form characterizations, even when exponential file size distributions are assumed. For more general file size distributions, the diffusion approximation was derived for the equal-weights case by Vlasiou, Zhang and Zwart (2014), but an interchange-of-limits result was lacking. We take a Lyapunov-drift-based approach that is different from the diffusion approximation approach, where we directly analyze the steady state of the system. We first establish a state-space collapse result in steady state, and then obtain explicit-form bounds on the weighted sum of the expected numbers of flows on different routes , where the weights are the same as those used in the weighted proportionally fair sharing policy.
Revised:  However, except for the case where the weights of all the routes are equal, the steady-state distribution of the limiting diffusion process is unknown and thus there are no explicit-form bounds on the weighted sum of the expected numbers of flows on different routes , where the weights are the same as those used in the weighted proportionally fair sharing policy.
Edit intent: coherence
Original:  We first establish a state-space collapse result in steady state, and then obtain explicit-form bounds on the weighted sum of the expected numbers of flows on different routes , where the weights are the same as those used in the weighted proportionally fair sharing policy. Our bounds hold for a class of phase-type file size distributions;
Revised:  We first establish a state-space collapse result in steady state, and then obtain explicit-form bounds on the weighted sum of the expected numbers of flows on different routes in heavy traffic. The bounds are linear in the number of critically loaded links in the network, and they hold for a class of phase-type file size distributions;
Edit intent: meaning-changed