wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Furthermore, we describe an%DIFDELCMD < \widetilde{O}%%% (mn^{\omega+1 + n^{2\omega+2}) algorithm for finding a suitably approximate John's ellipsoid for a symmetric polytope based on Vaidya's algorithm, and show the mixing time is retained using these approximate ellipsoids (where \omega < 2.373 is the current value of the fast matrix multiplication constant)}  containing x, }\\{|q-x|}\ is bounded above by a polynomial in n} .
Revised:  Furthermore, we describe an%DIFDELCMD < \widetilde{O}%%% + n^{2\omega+2}) algorithm for finding a suitably approximate John's ellipsoid for a symmetric polytope based on Vaidya's algorithm, and show the mixing time is retained using these approximate ellipsoids (where \omega < 2.373 is the current value of the fast matrix multiplication constant)} containing x, }\\{|q-x|}\ is bounded above by a polynomial in n} .
Edit intent: clarity
Original:  Furthermore, we describe an%DIFDELCMD < \widetilde{O}%%% (mn^{\omega+1 + n^{2\omega+2}) algorithm for finding a suitably approximate John's ellipsoid for a symmetric polytope based on Vaidya's algorithm, and show the mixing time is retained using these approximate ellipsoids (where \omega < 2.373 is the current value of the fast matrix multiplication constant)}  containing x, }\\{|q-x|}\ is bounded above by a polynomial in n} .
Revised:  Furthermore, we describe an%DIFDELCMD < \widetilde{O}%%% (mn^{\omega+1 + n^{2\omega+2}) algorithm for finding a suitably approximate John's ellipsoid for a symmetric polytope based on Vaidya's algorithm, and show the mixing time is retained using these approximate ellipsoids (where \omega < 2.373 is the current value of the fast matrix multiplication constant)} desired total variation distance to uniformity. We also prove polynomial mixing bounds starting from any fixed point x such that for any chord pq of \mathcal{K containing x, }\\{|q-x|}\ is bounded above by a polynomial in n} .
Edit intent: meaning-changed
Original:  Furthermore, we describe an%DIFDELCMD < \widetilde{O}%%% (mn^{\omega+1 + n^{2\omega+2}) algorithm for finding a suitably approximate John's ellipsoid for a symmetric polytope based on Vaidya's algorithm, and show the mixing time is retained using these approximate ellipsoids (where \omega < 2.373 is the current value of the fast matrix multiplication constant)}  containing x, }\\{|q-x|}\ is bounded above by a polynomial in n} .
Revised:  Furthermore, we describe an%DIFDELCMD < \widetilde{O}%%% (mn^{\omega+1 + n^{2\omega+2}) algorithm for finding a suitably approximate John's ellipsoid for a symmetric polytope based on Vaidya's algorithm, and show the mixing time is retained using these approximate ellipsoids (where \omega < 2.373 is the current value of the fast matrix multiplication constant)} containing x, }\\log \frac{|p-x|{|q-x|}\ is bounded above by a polynomial in n} .
Edit intent: meaning-changed
Original: In this extended abstract, we first present a PTAS for guarding the vertices of a weakly-visible polygon P from a subset of its vertices, or in other words, a PTAS for computing a minimum dominating set of the visibility graph of the vertices of P.
Revised: In this extended abstract, we present a PTAS for guarding the vertices of a weakly-visible polygon P from a subset of its vertices, or in other words, a PTAS for computing a minimum dominating set of the visibility graph of the vertices of P.
Edit intent: coherence
Original:  The usual way to get uniqueness is to assume the function is strictly quasiconvex and the domain is convex. Outside of a few special cases, verifying uniqueness without convexity has not been done and is often just assumed. The main result of this paper establishes uniqueness without assuming convexity by relying on an easy-to-verify nondegeneracy condition. The main result of this paper has widespread application beyond econometrics. Six applications are discussed : uniqueness of M-estimators, utility maximization with a nonconvex budget set, uniqueness of the policy function in dynamic programming, envelope theorems, limit theory in weakly identified models, and functionals of Brownian motion .
Revised:  This paper first formulates a general result that proves almost sure uniqueness without convexity of the objective function. The general result is then applied to a variety of applications in statistics. Four applications are discussed : uniqueness of M-estimators, utility maximization with a nonconvex budget set, uniqueness of the policy function in dynamic programming, envelope theorems, limit theory in weakly identified models, and functionals of Brownian motion .
Edit intent: meaning-changed
Original:  Six applications are discussed : uniqueness of M-estimators, utility maximization with a nonconvex budget set, uniqueness of the policy function in dynamic programming, envelope theorems, limit theory in weakly identified models, and functionals of Brownian motion .
Revised:  Six applications are discussed , including uniqueness of M-estimators, utility maximization with a nonconvex budget set, uniqueness of the policy function in dynamic programming, envelope theorems, limit theory in weakly identified models, and functionals of Brownian motion .
Edit intent: clarity
Original:  Six applications are discussed : uniqueness of M-estimators, utility maximization with a nonconvex budget set, uniqueness of the policy function in dynamic programming, envelope theorems, limit theory in weakly identified models, and functionals of Brownian motion .
Revised:  Six applications are discussed : uniqueness of M-estimators, both classical likelihood and penalized likelihood estimators, and two applications of the argmin theorem, threshold regression and weak identification .
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Original:  This type of optimization problems is characterized by a constraint ofinfinity -dimension, that is, the derivatives of the decision quantile functions are bounded. Such a constraint essentially comes from the "incentive compatibility" constraint for any optimal insurance contract to avoid the potential severe problem of moral hazardin insurance contract design models. By a further development of the author's relaxation method, this paper provides a systemic approach to solving this new type of quantile optimization problems }  .  The optimal quantile is expressed via the solution of a free boundary problem for a  second-order nonlinear ordinary differential equation (ODE), which is similar to the Black-Scholes ODE for perpetual American options and has been well studied in literature theoretically and numerically .
Revised:  This type of optimization problems is characterized by a constraint ofinfinity problem under rank-dependent utility (RDU) theory. Their results, however, suffer from a moral hazard problem, namely, providing incentives for the insured to falsely report the actual loss. Xu et al. (2019) investigated the same problem, but took the } . The optimal quantile is expressed via the solution of a free boundary problem for a second-order nonlinear ordinary differential equation (ODE), which is similar to the Black-Scholes ODE for perpetual American options and has been well studied in literature theoretically and numerically .
Edit intent: meaning-changed
Original:  By a further development of the author's relaxation method, this paper provides a systemic approach to solving this new type of quantile optimization problems }  .  The optimal quantile is expressed via the solution of a free boundary problem for a  second-order nonlinear ordinary differential equation (ODE), which is similar to the Black-Scholes ODE for perpetual American options and has been well studied in literature theoretically and numerically .
Revised:  By a further development of the author's relaxation method, this paper provides a systemic approach to solving this new type of quantile optimization problems incentive compatibility} . The optimal quantile is expressed via the solution of a free boundary problem for a second-order nonlinear ordinary differential equation (ODE), which is similar to the Black-Scholes ODE for perpetual American options and has been well studied in literature theoretically and numerically .
Edit intent: coherence
Original:  By a further development of the author's relaxation method, this paper provides a systemic approach to solving this new type of quantile optimization problems }  .  The optimal quantile is expressed via the solution of a free boundary problem for a  second-order nonlinear ordinary differential equation (ODE), which is similar to the Black-Scholes ODE for perpetual American options and has been well studied in literature theoretically and numerically .
Revised:  By a further development of the author's relaxation method, this paper provides a systemic approach to solving this new type of quantile optimization problems } constraint into consideration to avoid that moral hazard . The optimal quantile is expressed via the solution of a free boundary problem for a second-order nonlinear ordinary differential equation (ODE), which is similar to the Black-Scholes ODE for perpetual American options and has been well studied in literature theoretically and numerically .
Edit intent: meaning-changed
Original:  By a further development of the author's relaxation method, this paper provides a systemic approach to solving this new type of quantile optimization problems }  .  The optimal quantile is expressed via the solution of a free boundary problem for a  second-order nonlinear ordinary differential equation (ODE), which is similar to the Black-Scholes ODE for perpetual American options and has been well studied in literature theoretically and numerically .
Revised:  By a further development of the author's relaxation method, this paper provides a systemic approach to solving this new type of quantile optimization problems } . Mathematically speaking, the model reduces to a quantile optimisation problem with a compatibility constraint. They solved the problem by imposing assumptions on the loss and the probability weighting function. This paper solves the problem completely by a new quantile optimisation approach under general setting. The optimal quantile is expressed via the solution of a free boundary problem for a second-order nonlinear ordinary differential equation (ODE), which is similar to the Black-Scholes ODE for perpetual American options and has been well studied in literature theoretically and numerically .
Edit intent: meaning-changed
Original:  By a further development of the author's relaxation method, this paper provides a systemic approach to solving this new type of quantile optimization problems }  .  The optimal quantile is expressed via the solution of a free boundary problem for a  second-order nonlinear ordinary differential equation (ODE), which is similar to the Black-Scholes ODE for perpetual American options and has been well studied in literature theoretically and numerically .
Revised:  By a further development of the author's relaxation method, this paper provides a systemic approach to solving this new type of quantile optimization problems } . The optimal solution is expressed by the solution of a free boundary problem for a second-order nonlinear ordinary differential equation (ODE), which is similar to the Black-Scholes ODE for perpetual American options and has been well studied in literature theoretically and numerically .
Edit intent: fluency
Original:  By a further development of the author's relaxation method, this paper provides a systemic approach to solving this new type of quantile optimization problems }  .  The optimal quantile is expressed via the solution of a free boundary problem for a  second-order nonlinear ordinary differential equation (ODE), which is similar to the Black-Scholes ODE for perpetual American options and has been well studied in literature theoretically and numerically .
Revised:  By a further development of the author's relaxation method, this paper provides a systemic approach to solving this new type of quantile optimization problems } . The optimal quantile is expressed via the solution of an obstacle problem for a second-order nonlinear ordinary differential equation (ODE), which is similar to the Black-Scholes ODE for perpetual American options and has been well studied in literature theoretically and numerically .
Edit intent: clarity
Original:  By a further development of the author's relaxation method, this paper provides a systemic approach to solving this new type of quantile optimization problems }  .  The optimal quantile is expressed via the solution of a free boundary problem for a  second-order nonlinear ordinary differential equation (ODE), which is similar to the Black-Scholes ODE for perpetual American options and has been well studied in literature theoretically and numerically .
Revised:  By a further development of the author's relaxation method, this paper provides a systemic approach to solving this new type of quantile optimization problems } . The optimal quantile is expressed via the solution of a free boundary problem for a semilinear second-order nonlinear ordinary differential equation (ODE), which is similar to the Black-Scholes ODE for perpetual American options and has been well studied in literature theoretically and numerically .
Edit intent: meaning-changed
Original:  By a further development of the author's relaxation method, this paper provides a systemic approach to solving this new type of quantile optimization problems }  .  The optimal quantile is expressed via the solution of a free boundary problem for a  second-order nonlinear ordinary differential equation (ODE), which is similar to the Black-Scholes ODE for perpetual American options and has been well studied in literature theoretically and numerically .
Revised:  By a further development of the author's relaxation method, this paper provides a systemic approach to solving this new type of quantile optimization problems } . The optimal quantile is expressed via the solution of a free boundary problem for a second-order elliptic operator with mixed boundary conditions. Surprisingly, it is shown that every reasonable moral-hazard-free contract is optimal for infinitely many RDU maximisers with different utility functions and probability weighting functions .
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Original:  This allows to approximate the Ising distribution by a simpler model where the latent variables follow a multivariate normal distribution . The resulting approximation bears similarities with the Thouless Anderson Palmer (TAP) solution from mean field theory, but retains a broader range of applicability when the coupling weights are not independently distributed. Moreover, unlike classic mean field approaches, the approximation can be used to generate correlated spin patterns .
Revised:  This allows to approximate the Ising distribution by a simpler model where the latent variables follow a multivariate normal distribution , the so-called Cox distribution. The approximation is formally related to an advanced mean field technique known as adaptive TAP, and its domain of validity is similar. When valid, it allows a principled replacement of the Ising distribution by a distribution much easier to sample and manipulate .
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Original: It is shown that the Ising distribution can be treated as a latent variable model, where a set of N real-valued, correlated random variables are drawn and used to generate N binary spins independently. This allows to approximate the Ising distribution by a simpler model where the latent variables follow a multivariate normal distribution , the so-called Cox distribution.
Revised: During the past decades, the Ising distribution has attracted interest in many applied disciplines, as the maximum entropy distribution associated to any set of correlated binary (`spin') variables with observed means and covariances. However, numerically speaking, the Ising distribution is unpractical, so alternative models are often preferred to handle correlated binary data. One popular alternative, especially in life sciences, is the Cox distribution (or the closely related dichotomized Gaussian distribution and log-normal Cox point process), where the spins are generated independently conditioned on the drawing of a latent variable with a multivariate normal distribution , the so-called Cox distribution.
Edit intent: meaning-changed
Original:  The approximation is formally related to an advanced mean field technique known as adaptive TAP, and its domain of validity is similar. When valid, it allows a principled replacement of the Ising distribution by a distribution much easier to sample and manipulate .
Revised:  It shows that the Ising distribution itself can be treated as a latent variable model, and it explores when this latent variable has a quasi-normal distribution. A variational approach to this question reveals a formal link with classic mean-field methods, especially Opper and Winther's adaptive TAP approximation. This link is confirmed by weak coupling (Plefka) expansions of the different approximations and then by numerical tests. Overall, this study suggests that an Ising distribution can be replaced by a Cox distribution in practical applications, precisely when its parameters lie in the `mean-field domain' .
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Original:  For this reason, quantifying the shape of districts, in particular their compactness, is a key task in politics and civil rights. A growing body of literature suggests and analyzes compactness measures mathematically, but little consideration has been given to how these scores should be calculated in practice. Here, we consider the effects of a number of decisionsthat must be made in interpreting and implementing a set of popular compactness scores. We show that the choices made in quantifying compactness may themselves become political tools, with seemingly innocuous decisions leading to disparate scores. We show that when the full range of implementation flexibility is used, it can be abused to make clearly gerrymandered districts appear quantitatively reasonable. This complicates using compactness as a legislative or judicial standard to counteract unfair redistricting practices.
Revised:  A number of measurements have been suggested as ways to detect and prevent such behavior. These measures give concrete axes along which districts and districting plans can be compared. However, measurement values are affected by both noise and the compounding effects of seemingly innocuous implementation decisions. Such issues will arise for any measure. As a case study demonstrating the effect, we show that commonly-used measures of geometric compactness for district boundaries are affected by several factors irrelevant to fairness or compliance with civil rights law. We further show that an adversary could manipulate measurements to affect the assessment of a given plan. This instability complicates using these measurements as legislative or judicial standard to counteract unfair redistricting practices.
Edit intent: coherence
Original:  We present a polynomial time algorithm to compute the bottleneck distance for these modules from indecomposables, which bounds the interleaving distance from above, and give another algorithm to compute a new distance called {\em dimension distance} that bounds it from below  .
Revised:  We present a polynomial time algorithm to compute the bottleneck distance for these modules from indecomposables, which bounds the interleaving distance from above, and give another algorithm to compute a new distance called {\em dimension distance} that bounds it from below . An earlier version of this paper considered only the 2-parameter interval decomposable modules~\mbox{%DIFAUXCMD DeyCheng18 .
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Original:  We uncover variations of country- and transaction-based nestedness over time, and identify the countries and industries that most contributed to nestedness by assessing the effects of the removal of nodes and layers on the participation matrices .
Revised:  Drawing on appropriate null models that preserve the countries' or layers' degree distributions in the original multi-layer network, we uncover variations of country- and transaction-based nestedness over time, and identify the countries and industries that most contributed to nestedness by assessing the effects of the removal of nodes and layers on the participation matrices .
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Original:  We formulate strain identification as an inverse problem that aims at simultaneously estimating a binary matrix (encoding presence or absence of mutations  ) and a real-valued vector (representing the mixture of strains) such that their product is approximately equal to the measured data vector.
Revised:  We formulate strain identification as an inverse problem that aims at simultaneously estimating a binary matrix (encoding presence or absence of mutations in each strain ) and a real-valued vector (representing the mixture of strains) such that their product is approximately equal to the measured data vector.
Edit intent: meaning-changed
Original:  Such a family forms the reaction part of a  stochastic reaction-diffusion system when we insert a local Mexican Hat-type, difference of Gaussians, coupling on a one-dimensional and on a two-dimensional lattice.
Revised:  Such a family performs the reaction part of a stochastic reaction-diffusion system when we insert a local Mexican Hat-type, difference of Gaussians, coupling on a one-dimensional and on a two-dimensional lattice.
Edit intent: clarity
Original:  Such a family forms the reaction part of a  stochastic reaction-diffusion system when we insert a local Mexican Hat-type, difference of Gaussians, coupling on a one-dimensional and on a two-dimensional lattice.
Revised:  Such a family forms the reaction part of a discrete stochastic reaction-diffusion system when we insert a local Mexican Hat-type, difference of Gaussians, coupling on a one-dimensional and on a two-dimensional lattice.
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Original:  We find spatial patterns of oscillating quasi-cycles that resemble Turing patterns , called quasi-patterns.
Revised:  Quasi-cycles are a proposed mechanism for the production of neural oscillations, and Mexican Hat coupling is ubiquitous in the brain. Thus this combination might provide insight into the function of neural oscillations in the brain. Importantly, we study this system only in the transient case, on time intervals before saturation occurs. In one dimension, for weak coupling, we find that the phases of the coupled quasi-cycles synchronize (establish a relatively constant relationship, or phase lock) rapidly at coupling strengths lower than those required to produce spatial patterns of oscillating quasi-cycles that resemble Turing patterns , called quasi-patterns.
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Original:  We find spatial patterns of oscillating quasi-cycles that resemble Turing patterns , called quasi-patterns.
Revised:  We find spatial patterns of their amplitudes. In two dimensions the amplitude patterns form more quickly, but there remain parameter regimes in which phase synchronization patterns form without being accompanied by clear amplitude patterns. At higher coupling strengths we find patterns both of phase synchronization and of amplitude (resembling Turing patterns) corresponding to the patterns of phase synchronization.
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Original:  Specific properties of these patterns , such as local phase synchronization, can be predicted from the parameters of the reaction and of the Mexican Hat coupling . When the damping parameters of the reaction and diffusion parts are small and balanced, phase synchronization vanishes but amplitude patterns persist. These results extend our knowledge of the behaviour of coupled neural field equations and its dependence on stochastic fluctuations .
Revised:  Specific properties of these patterns , such as local phase synchronization, can be predicted from the parameters of the reaction and of the Mexican Hat coupling .
Edit intent: coherence