wanyu/IteraTeR_full_sent huggingface dataset:
Original: We prove that the Reeb space of a proper definable map  in an arbitrary o-minimal expansion of the reals is realizable as a proper definable quotient which can be seen as the definable analog of Stein factorization of proper morphisms in algebraic geometry.
Revised: We prove that the Reeb space of a proper definable map in an arbitrary o-minimal expansion of the reals is realizable as a proper definable quotient which can be seen as an o-minimal analog of Stein factorization of proper morphisms in algebraic geometry.
Edit intent: fluency
Original:  We also show that the Betti numbers of the Reeb space of a map f can be arbitrarily large compared to those of X, unlike in the special case of Reeb graphs of manifolds.
Revised:  We also show that the Betti numbers of the Reeb space of f can be arbitrarily large compared to those of X, unlike in the special case of Reeb graphs of manifolds.
Edit intent: clarity
Original:  Nevertheless, in the special case when f:X \rightarrow Y is a semi-algebraic map and X is closed and bounded, we prove a singly exponential upper bound on the Betti numbers of the Reeb space of f in terms of the number and degrees of the polynomials defining X,Y  and f.
Revised:  Nevertheless, in the special case when f:X \rightarrow Y is a semi-algebraic map and X is closed and bounded, we prove a singly exponential upper bound on the Betti numbers of the Reeb space of f in terms of the number and degrees of the polynomials defining X,Y , and f.
Edit intent: fluency
Original:  This leads us to a set of graph rules that enable us to determine fixed points for a CTLN that are independent of the parameters, and can be inferred directly from the underlying graph .
Revised:  This leads us to a set of graph rules that enable us to determine fixed points of a CTLN by analyzing the underlying graph. Additionally, we study larger networks composed of smaller "building block" subnetworks, and prove several theorems relating the fixed points of the full network to those of its components .
Edit intent: meaning-changed
Original:  As a step towards a probabilistic theory, we also show that for a random history indexed by a fixed galled tree and satisfying biologically reasonable conditions, the intervals of the 1st barcode are independent random variables.
Revised:  As a step towards a probabilistic theory, we also show that for a random history indexed by a fixed galled tree and satisfying biologically reasonable conditions, the intervals of the 1^{\mathrm{st barcode are independent random variables.
Edit intent: meaning-changed
Original: In this paper, we provide a parsimonious means to estimate panel VARs with stochastic volatility .
Revised: In this paper, we assess the impact of climate shocks on futures markets for agricultural commodities and a set of macroeconomic quantities for multiple high-income economies. To capture relations among countries, markets, and climate shocks, this paper proposes parsimonious methods to estimate high-dimensional panel VARs .
Edit intent: meaning-changed
Original:  We assume that coefficients associated with domestic lagged endogenous variables arise from a Gaussian mixture model . Shrinkage on the cluster size is introduced through suitable priors on the component weights and cluster-relevant quantities are identified through novel shrinkage priors . To assess whether dynamic interdependencies between economies are needed, we moreover impose shrinkage priors on the coefficients related to other countries' endogenous variables. Finally, our model controls for static interdependencies by assuming that the reduced form shocks of the model feature a factor stochastic volatility structure. We assess the merits of the proposed approach by using synthetic data as well as a real data application. In the empirical application, we forecast Eurozone unemployment rates and show that our proposed approach works well in terms of predictions .
Revised:  We assume that coefficients associated with domestic lagged endogenous variables arise from a Gaussian mixture model while further parsimony is achieved using suitable global-local shrinkage priors on several regions of the parameter space. Our results point towards pronounced global reactions of key macroeconomic quantities to climate shocks. Moreover, the empirical findings highlight substantial linkages between regionally located climate shifts and global commodity markets .
Edit intent: clarity
Original: In recent years, there is an increased interest in the role of static properties of and dynamics on signed graphs in physical, biological, and social networks.
Revised: Detecting and evaluating regions of brain under various circumstances is one of the most interesting topics in computational neuroscience. However, the majority of the studies on detecting communities of a functional connectivity network of the brain is done on networks obtained from coherency attributes, and not from correlation. This lack of studies, in part, is due to the role of static properties of and dynamics on signed graphs in physical, biological, and social networks.
Edit intent: meaning-changed
Original: In recent years, there is an increased interest in the role of static properties of and dynamics on signed graphs in physical, biological, and social networks. In particular, community structures of signed graphs and their modularity indices have drawn special attention, and there are numerous methods to identify them. Here we provide the technical details of implementing four important methods that in their nature are very different from one another; two spectral methods , one using the adjacency matrix and one using the Laplacian matrix, a heuristic graph theoretic method using a concept of edge centrality, and finally, a stochastic combinatorial optimization method. Because of the novel nature of the methods , we focus on an interesting problem of community structures in brain network of the CA1 region of the hippocampus of anesthetized rats to study the pre-ictal and post-ictal states.
Revised: In recent years, there is an increased interest in the fact that many common methods for clustering graphs require the nodes of the network to be `positively' linked together, a property that is guaranteed by a coherency matrix, by definition. However, correlation matrices reveal more information regarding how each pair of nodes are linked together. In this study, for the first time we simultaneously examine four inherently different network clustering methods (spectral, heuristic, and optimization methods) applied to the functional connectivity networks of the novel nature of the methods , we focus on an interesting problem of community structures in brain network of the CA1 region of the hippocampus of anesthetized rats to study the pre-ictal and post-ictal states.
Edit intent: meaning-changed
Original:  Because of the novel nature of the methods , we focus on an interesting problem of community structures in brain network of the CA1 region of the hippocampus of anesthetized rats to study the pre-ictal and post-ictal states.
Revised:  Because of the novel nature of the methods , we focus on an interesting problem of community structures in brain network of the CA1 region of the hippocampus of an anaesthetized rat during pre-ictal and post-ictal states.
Edit intent: clarity
Original:  We use recent electroenecephalograph (EEG) depth recordings for a period of 117 minutes at a sampling rate of 1000Hz. Since the electrode used has 16-contact points, we construct non-overlapping but sliding 100 , 000 sample-windowed correlation matricesor functional connectivity (FC) matrices over the recorded time, yielding signed graphs.
Revised:  The networks are obtained from correlation matrices , 000 sample-windowed correlation matricesor functional connectivity (FC) matrices over the recorded time, yielding signed graphs.
Edit intent: clarity
Original:  Since the electrode used has 16-contact points, we construct non-overlapping but sliding 100 , 000 sample-windowed correlation matricesor functional connectivity (FC) matrices over the recorded time, yielding signed graphs. Our results from the clustering methods both at the pre-ictal and post-ictal periods of the depth recording reported here for the first time yield convincing answers to differing community structures .
Revised:  Since the electrode used has 16-contact points, we construct non-overlapping but sliding 100 , and its results are compared with the ones obtained by applying the same methods to coherency matrices. The correlation matrices show a much finer community structure compared to the coherency matrices. Furthermore, we examine the potential smoothing effect of choosing various window sizes for computing the correlation/coherency matrices .
Edit intent: clarity
Original:  Under shape misspecification of the conditional mean and variance functions, we establish existence and uniqueness of the resulting approximations and characterize their formal interpretation . We illustrate our method with numerical simulations and two empirical applications to the estimation of the relationship between economic prosperity in 1500 and today, and demand for gasoline in the United States.
Revised:  Under shape misspecification of the conditional mean and variance functions, we establish existence and uniqueness of the resulting approximations and characterize their formal interpretation and robustness properties. In particular, we show that the corresponding mean-variance regression location-scale model weakly dominates the ordinary least-squares location model under a Kullback-Leibler measure of divergence, with strict improvement in the presence of heteroskedasticity. The simultaneous mean-variance regression loss function is globally convex and the corresponding estimator is easy to implement. We establish its consistency and asymptotic normality under misspecification, provide robust inference methods, and present numerical simulations that show large improvements over ordinary and weighted least-squares in terms of estimation and inference in finite samples. We further illustrate our method with numerical simulations and two empirical applications to the estimation of the relationship between economic prosperity in 1500 and today, and demand for gasoline in the United States.
Edit intent: meaning-changed
Original:  In this paper I show that selecting asset positions to maximize expected quadratic utility is equivalent to a machine learning (ML) problem , where the asset weights are chosen to minimize out of sample mean squared error .
Revised:  In this paper I show that selecting asset positions to maximize expected quadratic utility is equivalent to a machine learning (ML) problem , where the outcome to be predicted is a constant and the vector of explanatory variables is the asset returns .
Edit intent: meaning-changed
Original:  It follows that ML specifically targets estimation risk when choosing the asset weights, and that "off-the-shelf" ML algorithms obtain optimal portfolios taking parameter uncertaintyinto account. Linear regression is a special case of the proposed ML framework , equivalent to the traditional approach . Standard results from the machine learning literaturemay be used to derive conditions for when ML algorithms improve upon linear regression . Based on simulation studies and several datasets, I find that ML significantly reduce estimation risk compared to  the traditional approach and several shrinkage approaches proposed in the literature .
Revised:  It follows that ML specifically targets estimation risk when choosing the asset weights, and that "off-the-shelf" ML algorithms can be used to estimate the optimal portfolio in the presence of parameter uncertainty. The framework nests the traditional approach . Standard results from the machine learning literaturemay be used to derive conditions for when ML algorithms improve upon linear regression . Based on simulation studies and several datasets, I find that ML significantly reduce estimation risk compared to the traditional approach and several shrinkage approaches proposed in the literature .
Edit intent: clarity
Original:  Linear regression is a special case of the proposed ML framework , equivalent to the traditional approach . Standard results from the machine learning literaturemay be used to derive conditions for when ML algorithms improve upon linear regression . Based on simulation studies and several datasets, I find that ML significantly reduce estimation risk compared to  the traditional approach and several shrinkage approaches proposed in the literature .
Revised:  Linear regression is a special case of the proposed ML framework , equivalent to the traditional approach and recently proposed shrinkage approaches as special cases. By relying on results from the machine learning literaturemay be used to derive conditions for when ML algorithms improve upon linear regression . Based on simulation studies and several datasets, I find that ML significantly reduce estimation risk compared to the traditional approach and several shrinkage approaches proposed in the literature .
Edit intent: meaning-changed
Original:  Linear regression is a special case of the proposed ML framework , equivalent to the traditional approach . Standard results from the machine learning literaturemay be used to derive conditions for when ML algorithms improve upon linear regression . Based on simulation studies and several datasets, I find that ML significantly reduce estimation risk compared to  the traditional approach and several shrinkage approaches proposed in the literature .
Revised:  Linear regression is a special case of the proposed ML framework , equivalent to the traditional approach . Standard results from the ML literature, I derive new insights for existing approaches and propose new estimation methods . Based on simulation studies and several datasets, I find that ML significantly reduce estimation risk compared to the traditional approach and several shrinkage approaches proposed in the literature .
Edit intent: meaning-changed
Original:  Linear regression is a special case of the proposed ML framework , equivalent to the traditional approach . Standard results from the machine learning literaturemay be used to derive conditions for when ML algorithms improve upon linear regression . Based on simulation studies and several datasets, I find that ML significantly reduce estimation risk compared to  the traditional approach and several shrinkage approaches proposed in the literature .
Revised:  Linear regression is a special case of the proposed ML framework , equivalent to the traditional approach . Standard results from the machine learning literaturemay be used to derive conditions for when ML algorithms improve upon linear regression . Based on simulation studies and several datasets, I find that ML significantly reduces estimation risk compared to the traditional approach and several shrinkage approaches proposed in the literature .
Edit intent: fluency
Original:  Linear regression is a special case of the proposed ML framework , equivalent to the traditional approach . Standard results from the machine learning literaturemay be used to derive conditions for when ML algorithms improve upon linear regression . Based on simulation studies and several datasets, I find that ML significantly reduce estimation risk compared to  the traditional approach and several shrinkage approaches proposed in the literature .
Revised:  Linear regression is a special case of the proposed ML framework , equivalent to the traditional approach . Standard results from the machine learning literaturemay be used to derive conditions for when ML algorithms improve upon linear regression . Based on simulation studies and several datasets, I find that ML significantly reduce estimation risk compared to both the traditional approach and several shrinkage approaches proposed in the literature .
Edit intent: clarity
Original:  Linear regression is a special case of the proposed ML framework , equivalent to the traditional approach . Standard results from the machine learning literaturemay be used to derive conditions for when ML algorithms improve upon linear regression . Based on simulation studies and several datasets, I find that ML significantly reduce estimation risk compared to  the traditional approach and several shrinkage approaches proposed in the literature .
Revised:  Linear regression is a special case of the proposed ML framework , equivalent to the traditional approach . Standard results from the machine learning literaturemay be used to derive conditions for when ML algorithms improve upon linear regression . Based on simulation studies and several datasets, I find that ML significantly reduce estimation risk compared to the traditional approach and the equal weight strategy .
Edit intent: meaning-changed
Original:  It is assumed that the brain makes an internal estimate of an individual's own evolutionary fitness, which can be shown to produce an irreducible, distinct cause . Communicating components of the fitness estimate (either for external or internal use) requires inverting them.
Revised:  It is assumed that the brain makes an internal estimate of an individual's own evolutionary fitness, which can be shown to produce a special, distinct form of causation . Communicating components of the fitness estimate (either for external or internal use) requires inverting them.
Edit intent: clarity
Original: This paperprovides a new methodology to analyze unobserved heterogeneity when observed characteristics are modeled nonlinearly. The proposed modelbuilds on varying random coefficients(VRC) that are determined by nonlinear functions of observed regressors and additively separable unobservables. This paper proposes a novel estimator of the VRC density based on weighted sieve minimum distance. The main example of sieve bases are Hermite functions which yield a numerically stable estimation procedure.This paper shows inference results that go beyond what has been shown in ordinary RC models: Only estimation of the joint VRC density is affected by ill-posedness but not that of the varying randomslope (VRS) density. We provide in each case the optimal rate of convergence and also establish pointwise limit theory of linear functionals, where a prominent example is the density of potential outcomes. In addition, a multiplier bootstrap procedure is proposed to construct uniform confidence bands.
Revised: In this paper, we suggest and analyze a new class of specification tests for random coefficient models. These tests allow to assess the validity of central structural features of the model, in particular linearity in coefficients, generalizations of this notion like a known nonlinear functional relationship, or degeneracy of the distribution of a multiplier bootstrap procedure is proposed to construct uniform confidence bands.
Edit intent: meaning-changed
Original:  In addition, a multiplier bootstrap procedure is proposed to construct uniform confidence bands. A Monte Carlo study examines finite sample properties of the estimator and shows that it performs well even when the regressors associated to RC are far from being heavy tailed. Finally, the methodology is applied to analyze heterogeneity in income elasticity of demand for housing .
Revised:  In addition, a random coefficient, i.e., whether a coefficient is fixed or random, including whether an associated variable can be omitted altogether. Our tests are nonparametric in nature, and use sieve estimators of the characteristic function. We provide formal power analysis against global as well as against local alternatives. Moreover, we perform a Monte Carlo simulation study, and apply the tests to analyze the degree of nonlinearity in a heterogeneous random coefficients demand model. While we find some evidence against the popular QUAIDS specification with random coefficients, it is not strong enough to reject the specification at the conventional significance level .
Edit intent: meaning-changed
Original: In this paper , we suggest and analyze a new class of specification tests for random coefficient models. These tests allow to assess the validity of central structural features of the model , in particular linearity in coefficients , generalizations of this notion like a known nonlinear functional relationship, or degeneracy of the distribution of a random coefficient, i. e. , whether a coefficient is fixed or random, including whether an associated variable can be omitted altogether.
Revised: This paper provides a new methodology to analyze unobserved heterogeneity when observed characteristics are modeled nonlinearly. The proposed model builds on varying random coefficients (VRC) that are determined by nonlinear functions of observed regressors and additively separable unobservables. This paper proposes a novel estimator of the VRC density based on weighted sieve minimum distance. The main example of sieve bases are Hermite functions which yield a numerically stable estimation procedure. This paper shows inference results that go beyond what has been shown in ordinary RC models. We provide in each case rates of convergence and also establish pointwise limit theory of linear functionals, where a prominent example is the density of potential outcomes. In addition, a random coefficient, i. e. , whether a coefficient is fixed or random, including whether an associated variable can be omitted altogether.
Edit intent: meaning-changed
Original:  These tests allow to assess the validity of central structural features of the model , in particular linearity in coefficients , generalizations of this notion like a known nonlinear functional relationship, or degeneracy of the distribution of a random coefficient, i. e. , whether a coefficient is fixed or random, including whether an associated variable can be omitted altogether. Our tests are nonparametric in nature, and use sieve estimators of the characteristic function. We provide formal power analysis against global as well as against local alternatives. Moreover, we perform a Monte Carlo simulation study , and apply the tests to analyze the degree of nonlinearity in a heterogeneous random coefficients demand model. While we find some evidence against the popular QUAIDS specification with random coefficients, it is not strong enough to reject the specification at the conventional significance level .
Revised:  These tests allow to assess the validity of central structural features of the model , in particular linearity in coefficients , generalizations of this notion like a known nonlinear functional relationship, or degeneracy of the distribution of a multiplier bootstrap procedure is proposed to construct uniform confidence bands. A Monte Carlo study examines finite sample properties of the estimator and shows that it performs well even when the regressors associated to RC are far from being heavy tailed. Finally, the methodology is applied to analyze heterogeneity in income elasticity of demand for housing .
Edit intent: meaning-changed
Original: We examine the problem of transforming matching collections of data points into optimal correspondence. The classic RMSD (root-mean-square deviation) method calculates a 3D rotation that minimizes the RMSD of a set of test data points relative to a reference set of corresponding points. Similar literature in aeronautics, photogrammetry, and proteomics employs numerical methods to find the maximal eigenvalue of a particular 4\!\times\! 4 quaternion-based matrix, thus specifying the quaternion eigenvector corresponding to the optimal 3D rotation.
Revised: We review the general problem of finding a global rotation that transforms a given set of points and/or coordinate frames (the "test" data) into the best possible alignment with a corresponding set (the "reference" data). For 3D rotation.
Edit intent: clarity