wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We present an algorithm for the case where mutations are restricted to pure strategies . This is the first positive result for computation of ESS, as all prior results are computational hardness and no prior algorithms have been presented .
Revised:  We present an algorithm for the case where mutations are restricted to pure strategies , and present experiments on several game classes including random and a recently-proposed cancer model. Our algorithm is based on a mixed-integer non-convex feasibility program formulation, which constitutes the first general optimization formulation for this problem. It turns out that the vast majority of the games included in the experiments contain ESS with small support, and our algorithm is outperformed by a support-enumeration based approach. However we suspect our algorithm may be useful in the future as games are studied that have ESS with potentially larger and unknown support size .
Edit intent: meaning-changed
Original:  Moreover, to eliminate the ruin possibilities and having a minimum guarantee for the final annuity, we consider a safety level for the wealth process which consequently yields a Hamilton-Jacobi-Bellman (HJB) equation on a bounded domain.
Revised:  Moreover, to have a minimum guarantee for the final annuity, we consider a safety level for the wealth process which consequently yields a Hamilton-Jacobi-Bellman (HJB) equation on a bounded domain.
Edit intent: coherence
Original:  Moreover, to eliminate the ruin possibilities and having a minimum guarantee for the final annuity, we consider a safety level for the wealth process which consequently yields a Hamilton-Jacobi-Bellman (HJB) equation on a bounded domain.
Revised:  Moreover, to eliminate the ruin possibilities and having a minimum guarantee for the final annuity, a safety level for the wealth process which consequently yields a Hamilton-Jacobi-Bellman (HJB) equation on a bounded domain.
Edit intent: coherence
Original:  Moreover, to eliminate the ruin possibilities and having a minimum guarantee for the final annuity, we consider a safety level for the wealth process which consequently yields a Hamilton-Jacobi-Bellman (HJB) equation on a bounded domain.
Revised:  Moreover, to eliminate the ruin possibilities and having a minimum guarantee for the final annuity, we consider a safety level for the wealth process is considered. To solve the stochastic optimal control problem via dynamic programming, we obtain a Hamilton-Jacobi-Bellman (HJB) equation on a bounded domain.
Edit intent: meaning-changed
Original:  However, when solving the inverse problem -characterizing the structure behind a specific functional link- there are many possibilities with very different consequences. Excitation and inhibition, for instance, may each produce a causal dependence by coordinating neuronal populations, but inhibitory connections do not transmit information packages .
Revised:  However, each node is composed of many different elements which define the properties of the links. For instance, excitatory and inhibitory neuronal subtypes determine the functionality of the connection. Classic indexes such as the Granger causality (GC) quantifies these interactions, but they do not infer into the mechanism behind them .
Edit intent: clarity
Original:  Here, we introduce the concept of synaptic Granger causality (sGC), an extension of the well-known Granger causality approach that quantifies the ratio of excitatory/inhibitory projections involved in a functional link on the basis of the analysis of time series constructed using autoregressive models .
Revised:  Here, we introduce an extension of the well-known Granger causality approach that quantifies the ratio of excitatory/inhibitory projections involved in a functional link on the basis of the analysis of time series constructed using autoregressive models .
Edit intent: clarity
Original:  Here, we introduce the concept of synaptic Granger causality (sGC), an extension of the well-known Granger causality approach that quantifies the ratio of excitatory/inhibitory projections involved in a functional link on the basis of the analysis of time series constructed using autoregressive models .
Revised:  Here, we introduce the concept of synaptic Granger causality (sGC), an extension of the well-known GC that analyses the correlation associated to the specific influence that a transmitter node has over the receiver. This way, the G-causal link has a positive or negative effect if the predicted activity follows directly or inversely, respectively, the dynamics of the sender .
Edit intent: meaning-changed
Original:  The method is validated by using the membrane potential obtained from numerical simulations of neuronal motifs that mimic extracellular brain activity, similar to the experimentally measured local field potential. When excitatory and inhibitory synapses are not mixed, the method correctly predicts the type of synapses that participate in the signaling.
Revised:  The method is validated in a neuronal population model, testing the paradigm that excitatory and inhibitory synapses are not mixed, the method correctly predicts the type of synapses that participate in the signaling.
Edit intent: clarity
Original:  When excitatory and inhibitory synapses are not mixed, the method correctly predicts the type of synapses that participate in the signaling. Moreover, when both inputs project on the same neuron or population, the sGC estimates the proportion of both types of interaction .
Revised:  When excitatory and inhibitory neurons have a differential effect in the connectivity. Our approach correctly infers the positive or negative coupling produced by different types of neurons .
Edit intent: clarity
Original: In this paper we discuss a natural extension of infinite discrete partition-of-unity copulas to continuous partition of copulas which were recently introduced in the literature , with possible applications in risk management and other fields.
Revised: In this paper we discuss a natural extension of infinite discrete partition-of-unity copulas to continuous partition of copulas which were recently introduced in the literature to continuous partition of copulas with possible applications in risk management and other fields.
Edit intent: fluency
Original: Unraveling bacterial strategies for spatial exploration is crucial to understand the complexity of URLani- zation of life. Currently, a cornerstone for quantitative modeling of bacterial transport , is their run-and-tumble strategy to explore their environment .
Revised: Unraveling bacterial strategies for spatial exploration is crucial for understanding the complexity in URLanization of life. Bacterial motility determines the spatio-temporal structure of microbial communities, controls infection spreading and the URLanization in guts or in soils. Most theoretical approaches for modeling bacterial transport rely on their run-and-tumble strategy to explore their environment .
Edit intent: meaning-changed
Original:  For Escherichia coli, the run time distribution was reported to follow a Poisson process with a single characteristic time related to the rotational switching of the flagellar motor. Direct measurements on flagellar motors show , on the contrary, heavy-tailed distributions of rotation times stemming from the intrinsic noise in the chemotactic mechanism.
Revised:  For Escherichia coli, the run time distribution was reported to follow a Poisson process with a single characteristic time related to the rotational switching of the flagellar motors. However, direct measurements on flagellar motors show , on the contrary, heavy-tailed distributions of rotation times stemming from the intrinsic noise in the chemotactic mechanism.
Edit intent: coherence
Original:  This paper proposes  the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% ).
Revised: Alpha-based performance evaluation may fail to capture correlated residuals due to model errors. This paper proposes the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% ).
Edit intent: meaning-changed
Original:  This paper proposes  the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% ).
Revised:  This paper proposes using the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% ).
Edit intent: fluency
Original:  This paper proposes  the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% ).
Revised:  This paper proposes the Generalized Information Ratio (GIR) to measure performance under misspecified benchmarks . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% ).
Edit intent: clarity
Original:  This paper proposes  the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% ).
Revised:  This paper proposes the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% ).
Edit intent: fluency
Original:  This paper proposes  the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% ).
Revised:  This paper proposes the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix \Sigma%DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% ).
Edit intent: coherence
Original:  This paper proposes  the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% ).
Revised:  This paper proposes the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = %DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% ).
Edit intent: meaning-changed
Original:  This paper proposes  the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% ).
Revised:  This paper proposes the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% \alpha%DIFDELCMD < }%%% ).
Edit intent: coherence
Original:  This paper proposes  the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% ).
Revised:  This paper proposes the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% ^(-1/2) %DIFDELCMD < }%%% ).
Edit intent: coherence
Original:  This paper proposes  the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% ). GIR translates residual covariance information into adjusted alphas and nests alphas and Information Ratio as special cases . Simulation results show that GIR is robust to  model misspecification and produces stable out-of-sample returns.
Revised:  This paper proposes the Generalized Information Ratio (GIR) to evaluate the performance of active portfolios under misspecified models . Motivated by the theoretical link between abnormal returns and residual covariance matrix, GIR is derived as alphas scaled by the inverse square root of the residual covariance matrix (GIR = \Sigma%DIFDELCMD < }%%% ^(-1/2) \alpha%DIFDELCMD < }%%% . GIR nests alphas and Information Ratio as special cases . Simulation results show that GIR is robust to model misspecification and produces stable out-of-sample returns.
Edit intent: coherence
Original:  GIR translates residual covariance information into adjusted alphas and nests alphas and Information Ratio as special cases . Simulation results show that GIR is robust to  model misspecification and produces stable out-of-sample returns.
Revised:  GIR translates residual covariance information into adjusted alphas and nests alphas and Information Ratio as special cases , depending on the amount of information used in the residual covariance matrix. We show that GIR is robust to model misspecification and produces stable out-of-sample returns.
Edit intent: meaning-changed
Original:  GIR translates residual covariance information into adjusted alphas and nests alphas and Information Ratio as special cases . Simulation results show that GIR is robust to  model misspecification and produces stable out-of-sample returns.
Revised:  GIR translates residual covariance information into adjusted alphas and nests alphas and Information Ratio as special cases . Simulation results show that GIR is robust to various degrees of model misspecification and produces stable out-of-sample returns.
Edit intent: meaning-changed
Original: Leading terms of conditional bias and variance are useful when we tend to investigate the mean-square properties of locally weighted polynomial regression. In this paper, we consider a geographically weighted regression model with any d-dimensional locations and M-dimensional subscripts. Under a given structure of dependence and assumption of stationarity, based on a weight matrixcontrolled by euclidean distance function with scale parameters , we analyze the leading terms of conditional bias, variance of locally weighted pool least square estimationin each location .
Revised: It is widely known that geographically weighted regression(GWR) is essentially same as varying-coefficient model. In the former research about varying-coefficient model, scholars tend to use multidimensional-kernel-based locally weighted estimation(MLWE) so that information of both distance and direction is considered. However, when we construct the local weight matrix of geographically weighted estimation, distance among the locations in the neighbor is the only factor controlling the value of entries of weight matrix. In other word, estimation of GWR is distance-kernel-based. Thus, in this paper, under stationary and limited dependent data with multidimensional subscripts , we analyze the leading terms of conditional bias, variance of locally weighted pool least square estimationin each location .
Edit intent: meaning-changed
Original:  Under a given structure of dependence and assumption of stationarity, based on a weight matrixcontrolled by euclidean distance function with scale parameters , we analyze the leading terms of conditional bias, variance of locally weighted pool least square estimationin each location .
Revised:  Under a given structure of dependence and assumption of stationarity, based on a weight matrixcontrolled by euclidean distance function with scale parameters , we analyze the local mean squared properties of without any assumption of the form of coefficient functions and compare it with MLWE. According to the theoretical and simulation results, geographically-weighted locally linear estimation(GWLE) is asymptotically more efficient than MLWE .
Edit intent: meaning-changed
Original: We show that the Tverberg numberof \mathbb{Z^d and the intersection of convex hulls is required to have a non-empty intersection with S).
Revised: This paper discusses Tverberg-type theorems with coordinate constraints (i.e., versions of these theorems where all points lie within a subset S \subset \mathbb{R^d and the intersection of convex hulls is required to have a non-empty intersection with S).
Edit intent: meaning-changed
Original:  Doignon). We also present improvements on } the upper bounds for the Tverberg numbers of Z^3 and Z^j \times R^k  .
Revised:  Doignon). We also present improvements on } the upper bounds for the Tverberg numbers of Z^3 and Z^j \times R^k and an integer version of the well-known positive-fraction selection lemma of J. Pach .
Edit intent: meaning-changed
Original: We present an affine-invariant random walk for drawing uniform random samples from a convex body K \subset R^n for which the maximum volume inscribed ellipsoid , known as John's ellipsoid, may be computed.
Revised: We present an affine-invariant random walk for drawing uniform random samples from a convex body K \subset R^n that uses maximum volume inscribed ellipsoid , known as John's ellipsoid, may be computed.
Edit intent: clarity
Original: We present an affine-invariant random walk for drawing uniform random samples from a convex body K \subset R^n for which the maximum volume inscribed ellipsoid , known as John's ellipsoid, may be computed.
Revised: We present an affine-invariant random walk for drawing uniform random samples from a convex body K \subset R^n for which the maximum volume inscribed ellipsoids , known as John's ellipsoid, may be computed.
Edit intent: fluency
Original: We present an affine-invariant random walk for drawing uniform random samples from a convex body K \subset R^n for which the maximum volume inscribed ellipsoid , known as John's ellipsoid, may be computed. We consider a polytope \mathcal{P = \{x \in R^n \mid Ax \leq 1\} where A \in R^{m \times n} as a special case.
Revised: We present an affine-invariant random walk for drawing uniform random samples from a convex body K \subset R^n for which the maximum volume inscribed ellipsoid , known as John's = \{x \in R^n \mid Ax \leq 1\} where A \in R^{m \times n} as a special case.
Edit intent: clarity
Original:  We show that from a warm start, the random walk mixes in O(n^7) steps where the log factors depend only on constants determined by the warm start and error parameters (and not on the dimension or number of constraints defining the body).
Revised:  We show that from a warm start, the random walk mixes in O(n^7) steps where the log factors depend only on constants associated with the warm start and error parameters (and not on the dimension or number of constraints defining the body).
Edit intent: clarity
Original:  We show that from a warm start, the random walk mixes in O(n^7) steps where the log factors depend only on constants determined by the warm start and error parameters (and not on the dimension or number of constraints defining the body). This sampling algorithm thus offers improvement over the affine-invariant Dikin Walk for polytopes (which mixes in (mn) steps from a warm start) for applications in which m \gg n.
Revised:  We show that from a warm start, the random walk mixes in O(n^7) steps where the log factors depend only on constants determined by the warm start and (mn) steps from a warm start) for applications in which m \gg n.
Edit intent: coherence
Original:  This sampling algorithm thus offers improvement over the affine-invariant Dikin Walk for polytopes (which mixes in (mn) steps from a warm start) for applications in which m \gg n. 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:  This sampling algorithm thus offers improvement over the affine-invariant Dikin Walk for polytopes (which mixes in %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} .
Edit intent: clarity