wanyu/IteraTeR_full_sent huggingface dataset:
Original: Compared to physical systems that exhibit limited and mostly predetermined responses to external inputs, URLanisms show an enormous diversity of traits and an ability to evolve. Particular responses to different environmental conditions are developed URLanisms to adapt to varying environments. We study how such responses evolve by considering them as a mapping from environmental cues to phenotypic traits , modeled by a network with hidden units.
Revised: URLanisms exhibit diverse strategies for adapting to varying environments. For example, a population URLanisms may express the same phenotype in all environments (`unvarying strategy'), or follow environmental cues and express alternative phenotypes to match the environment (`tracking strategy'), or diversify into coexisting phenotypes to cope with environmental uncertainty (`bet-hedging strategy'). We introduce a general framework for studying URLanisms respond to environmental variations, which models an adaptation strategy by an abstract mapping from environmental cues to phenotypic traits , modeled by a network with hidden units.
Edit intent: meaning-changed
Original:  Depending on the accuracy of environmental cues and the strength of natural selection, we find different adaptation strategies characterized by the shape of phenotype distributions. In particular, three previously studied strategies emerge as special limits of our model:  when environmental cues are URLanisms rely on the cue to express the favorable phenotype in each environmental condition ("tracking strategy"), when cues are URLanisms either express a same phenotype in all environments ("unvarying strategy ") or, remarkably, use the uninformative cue as a source of randomness to diversify into subpopulations of different phenotypes ("bet-hedging strategy").
Revised:  Depending on the accuracy of environmental cues and the strength of natural selection, we find different adaptation strategies represented by mappings that maximize the longterm growth rate of a population. The previously studied strategies emerge as special limits of our model: when environmental cues are URLanisms rely on the cue to express the favorable phenotype in each environmental condition ("tracking strategy"), when cues are URLanisms either express a same phenotype in all environments ("unvarying strategy ") or, remarkably, use the uninformative cue as a source of randomness to diversify into subpopulations of different phenotypes ("bet-hedging strategy").
Edit intent: clarity
Original:  In particular, three previously studied strategies emerge as special limits of our model:  when environmental cues are URLanisms rely on the cue to express the favorable phenotype in each environmental condition ("tracking strategy"), when cues are URLanisms either express a same phenotype in all environments ("unvarying strategy ") or, remarkably, use the uninformative cue as a source of randomness to diversify into subpopulations of different phenotypes ("bet-hedging strategy").
Revised:  In particular, three previously studied strategies emerge as special cases of our model: when environmental cues are URLanisms rely on the cue to express the favorable phenotype in each environmental condition ("tracking strategy"), when cues are URLanisms either express a same phenotype in all environments ("unvarying strategy ") or, remarkably, use the uninformative cue as a source of randomness to diversify into subpopulations of different phenotypes ("bet-hedging strategy").
Edit intent: clarity
Original:  In particular, three previously studied strategies emerge as special limits of our model:  when environmental cues are URLanisms rely on the cue to express the favorable phenotype in each environmental condition ("tracking strategy"), when cues are URLanisms either express a same phenotype in all environments ("unvarying strategy ") or, remarkably, use the uninformative cue as a source of randomness to diversify into subpopulations of different phenotypes ("bet-hedging strategy").
Revised:  In particular, three previously studied strategies emerge as special limits of our model: the tracking strategy is favorable when environmental cues are URLanisms rely on the cue to express the favorable phenotype in each environmental condition ("tracking strategy"), when cues are URLanisms either express a same phenotype in all environments ("unvarying strategy ") or, remarkably, use the uninformative cue as a source of randomness to diversify into subpopulations of different phenotypes ("bet-hedging strategy").
Edit intent: meaning-changed
Original:  In particular, three previously studied strategies emerge as special limits of our model:  when environmental cues are URLanisms rely on the cue to express the favorable phenotype in each environmental condition ("tracking strategy"), when cues are URLanisms either express a same phenotype in all environments ("unvarying strategy ") or, remarkably, use the uninformative cue as a source of randomness to diversify into subpopulations of different phenotypes ("bet-hedging strategy").
Revised:  In particular, three previously studied strategies emerge as special limits of our model: when environmental cues are accurate, whereas when cues are URLanisms either express a same phenotype in all environments ("unvarying strategy ") or, remarkably, use the uninformative cue as a source of randomness to diversify into subpopulations of different phenotypes ("bet-hedging strategy").
Edit intent: clarity
Original:  In particular, three previously studied strategies emerge as special limits of our model:  when environmental cues are URLanisms rely on the cue to express the favorable phenotype in each environmental condition ("tracking strategy"), when cues are URLanisms either express a same phenotype in all environments ("unvarying strategy ") or, remarkably, use the uninformative cue as a source of randomness to diversify into subpopulations of different phenotypes ("bet-hedging strategy").
Revised:  In particular, three previously studied strategies emerge as special limits of our model: when environmental cues are URLanisms rely on the cue to express the favorable phenotype in each environmental condition ("tracking strategy"), when cues are URLanisms can either use an unvarying strategy or, remarkably, use the uninformative cue as a source of randomness to diversify into subpopulations of different phenotypes ("bet-hedging strategy").
Edit intent: clarity
Original:  In particular, three previously studied strategies emerge as special limits of our model:  when environmental cues are URLanisms rely on the cue to express the favorable phenotype in each environmental condition ("tracking strategy"), when cues are URLanisms either express a same phenotype in all environments ("unvarying strategy ") or, remarkably, use the uninformative cue as a source of randomness to diversify into subpopulations of different phenotypes ("bet-hedging strategy"). The capacity of exploring diverse responses and evolving different strategies is associated with having a high-dimensional internal representation of the environment.
Revised:  In particular, three previously studied strategies emerge as special limits of our model: when environmental cues are URLanisms rely on the cue to express the favorable phenotype in each environmental condition ("tracking strategy"), when cues are URLanisms either express a same phenotype in all environments ("unvarying strategy ") or, remarkably, use the uninformative cue as a source of randomness to bet-hedge. Our model of the environment-to-phenotype mapping is based on a network with hidden units; the performance of the strategies is shown to rely on having a high-dimensional internal representation of the environment.
Edit intent: meaning-changed
Original: For any constants d\ge 1, \epsilon >0, t>1, and any n-point set P\subsetR^d, we show that there is a geometric graph G=(P,E) having O(n\log ^4 n\log\log n) edges with the following property:
Revised: For any constants d\ge 1, \epsilon >0, t>1, and any n-point set P\subsetR^d, we show that there is a geometric graph G=(P,E) having O(n\log ^2 n\log\log n) edges with the following property:
Edit intent: meaning-changed
Original:  For any F\subseteq P, there exists F^+\supseteq F, |F^+| \le (1+\epsilon)|F| such that, for any pair p,q\in P\setminus F^+, the graph G-F contains a path from p to q whose (Euclidean) length is at most t times the Euclidean distance between p and q. In the terminology of robust spanners (Bose %DIFDELCMD < \etal%%% \ \et  2013) the graph G is a (1+\epsilon)k-robust t-spanner of P.
Revised:  For any F\subseteq P, there exists F^+\supseteq F, |F^+| \le (1+\epsilon)|F| such that, for any pair p,q\in P\setminus F^+, the graph G-F contains a path from p to q whose (Euclidean) length is at most t times the Euclidean distance between p and q. In the terminology of robust spanners (Bose %DIFDELCMD < \etal%%% \et 2013) the graph G is a (1+\epsilon)k-robust t-spanner of P.
Edit intent: fluency
Original:  For any F\subseteq P, there exists F^+\supseteq F, |F^+| \le (1+\epsilon)|F| such that, for any pair p,q\in P\setminus F^+, the graph G-F contains a path from p to q whose (Euclidean) length is at most t times the Euclidean distance between p and q. In the terminology of robust spanners (Bose %DIFDELCMD < \etal%%% \ \et  2013) the graph G is a (1+\epsilon)k-robust t-spanner of P.
Revised:  For any F\subseteq P, there exists F^+\supseteq F, |F^+| \le (1+\epsilon)|F| such that, for any pair p,q\in P\setminus F^+, the graph G-F contains a path from p to q whose (Euclidean) length is at most t times the Euclidean distance between p and q. In the terminology of robust spanners (Bose %DIFDELCMD < \etal%%% \ \et al, SICOMP, 42(4):1720--1736, 2013) the graph G is a (1+\epsilon)k-robust t-spanner of P.
Edit intent: meaning-changed
Original:  This construction is more sparse than the most recent work ( Buchin, Ol\`ah, and Har-Peled 2018) which proves the existence of (1+\epsilon)k-robust t-spanners with n\log^{O(d)} n edges.
Revised:  This construction is sparser than the recent constructions of Buchin, Ol\`ah, and Har-Peled 2018) which proves the existence of (1+\epsilon)k-robust t-spanners with n\log^{O(d)} n edges.
Edit intent: clarity
Original:  This construction is more sparse than the most recent work ( Buchin, Ol\`ah, and Har-Peled 2018) which proves the existence of (1+\epsilon)k-robust t-spanners with n\log^{O(d)} n edges.
Revised:  This construction is more sparse than the most recent work ( Buchin, Ol\`ah, and Har-Peled (arXiv:1811.06898) who prove the existence of (1+\epsilon)k-robust t-spanners with n\log^{O(d)} n edges.
Edit intent: meaning-changed
Original:  A common approach to modeling dynamic connectivity in resting-state whole-brain  fMRI is to compute (across moving temporal windows) the Pearson-correlation between anatomical regions derived from predefined brain parcellation.
Revised: Background: Recent studies have indicated that functional connectivity is dynamic even during rest. A common approach to modeling dynamic connectivity in resting-state whole-brain fMRI is to compute (across moving temporal windows) the Pearson-correlation between anatomical regions derived from predefined brain parcellation.
Edit intent: meaning-changed
Original:  A common approach to modeling dynamic connectivity in resting-state whole-brain  fMRI is to compute (across moving temporal windows) the Pearson-correlation between anatomical regions derived from predefined brain parcellation.
Revised:  A common approach to modeling the dynamic functional connectivity in whole-brain fMRI is to compute (across moving temporal windows) the Pearson-correlation between anatomical regions derived from predefined brain parcellation.
Edit intent: meaning-changed
Original:  A common approach to modeling dynamic connectivity in resting-state whole-brain  fMRI is to compute (across moving temporal windows) the Pearson-correlation between anatomical regions derived from predefined brain parcellation.
Revised:  A common approach to modeling dynamic connectivity in resting-state whole-brain resting-state fMRI is to compute (across moving temporal windows) the Pearson-correlation between anatomical regions derived from predefined brain parcellation.
Edit intent: meaning-changed
Original:  A common approach to modeling dynamic connectivity in resting-state whole-brain  fMRI is to compute (across moving temporal windows) the Pearson-correlation between anatomical regions derived from predefined brain parcellation. Due to image acquisition and physiological noise , the direct use of the sample correlation matrices is not reliable for the subsequent modeling of the dynamically-evolving connectivity matrices.
Revised:  A common approach to modeling dynamic connectivity in resting-state whole-brain fMRI is to compute (across moving temporal windows) the Pearson-correlation between anatomical regions via sliding time windows. However , the direct use of the sample correlation matrices is not reliable for the subsequent modeling of the dynamically-evolving connectivity matrices.
Edit intent: clarity
Original:  Due to image acquisition and physiological noise , the direct use of the sample correlation matrices is not reliable for the subsequent modeling of the dynamically-evolving connectivity matrices. To overcome this limitation , we propose a new regression approach that smooths out the noise by exploiting the geometric structure of correlation matrices.
Revised:  Due to image acquisition and physiological noise , the direct use of the sample correlation matrices is not reliable due to the image acquisition and processing noises in resting-sate fMRI. New method: To overcome these limitations , we propose a new regression approach that smooths out the noise by exploiting the geometric structure of correlation matrices.
Edit intent: meaning-changed
Original:  We demonstrate that the proposed method is useful for identifying distinct state spacesin the resting-state connectivities of males and females through the transition matrices of the common states .
Revised:  The dynamic correlation matrix is modeled as a linear combination of symmetric positive-definite matrices combined with cosine series representation. The resulting smoothed dynamic correlation matrices are clustered into disjoint brain connectivity states using the k-means clustering algorithm. Results: The proposed model preserves the geometric structure of underlying physiological dynamic correlation, eliminates unwanted noise in connectivity and obtains more accurate state spaces. The difference in the estimated dynamic connectivity states between males and females through the transition matrices of the common states .
Edit intent: meaning-changed
Original:  We demonstrate that the proposed method is useful for identifying distinct state spacesin the resting-state connectivities of males and females through the transition matrices of the common states .
Revised:  We demonstrate that the proposed method is useful for identifying distinct state spacesin the resting-state connectivities of males and females is identified. Comparison with existing methods: We demonstrate that the proposed statistical model has less rapid state changes caused by noise and improves the accuracy in identifying and discriminating different states. Conclusions: We propose a new regression model on dynamically changing correlation matrices that provides better performance over existing windowed correlation and is more reliable for the modeling of dynamic connectivity .
Edit intent: meaning-changed
Original: We investigate the problem of dynamic portfolio optimization in continuous-time, finite-horizon setting for a portfolio of two stocks and one risk-free asset. The stocks follow the Cointelation model. The proposed optimization methods are twofold. In what we call an Stochastic Differential Equation approach , we compute the optimal weights using mean-variance criterion and power utility maximization. We show that dynamically switching between these two optimal strategies by introducing a triggering function can further improve the portfolio returns. We contrast this with the machine learning clustering methodology inspired by the band-wise Gaussian mixture model. The first benefit of the machine learning over the Stochastic Differential Equation approach is that we were able to achieve the same results though a simpler channel. The second advantage is a flexibility to regime change & .
Revised: We investigate the problem of dynamic portfolio optimization in continuous-time, finite-horizon setting for a portfolio of two assets that are intertwined. In Financial Mathematics approach we model the asset prices not via the common approaches used in pairs trading such as a high correlation or cointegration, but with the cointelation model that aims to reconcile both short-term risk and long-term equilibrium. We maximize the overall P & .
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Original:  The second advantage is a flexibility to regime change & .
Revised:  The second advantage is a flexibility to regime change L with Financial Mathematics approach that dynamically switches between a mean-variance optimal strategy and a power utility maximizing strategy. We use a stochastic control formulation of the problem of power utility maximization and solve numerically the resulting HJB equation with the Deep Galerkin method. We turn to Machine Learning for the same P& .
Edit intent: meaning-changed
Original: Correlated component analysis (CORRCA) is a novel method for frequency recognition in steady-state visual evoked potential (SSVEP) based brain-computer interface (BCI), which holds the potential to implement high-performance SSVEP-based BCI systems.
Revised: Effective frequency recognition algorithms are critical in steady-state visual evoked potential (SSVEP) based brain-computer interface (BCI), which holds the potential to implement high-performance SSVEP-based BCI systems.
Edit intent: clarity
Original: Correlated component analysis (CORRCA) is a novel method for frequency recognition in steady-state visual evoked potential (SSVEP) based brain-computer interface (BCI), which holds the potential to implement high-performance SSVEP-based BCI systems.
Revised: Correlated component analysis (CORRCA) is a novel method for frequency recognition in steady-state visual evoked potential (SSVEP) based brain-computer interfaces (BCIs). In this study, we present a hierarchical feature fusion framework which can be used to design high-performance SSVEP-based BCI systems.
Edit intent: meaning-changed
Original: Correlated component analysis (CORRCA) is a novel method for frequency recognition in steady-state visual evoked potential (SSVEP) based brain-computer interface (BCI), which holds the potential to implement high-performance SSVEP-based BCI systems. CORRCA could provide multiple correlation coefficients to measure the correlation between two signals. However, only the largest one is selected as feature while ignoring all others in previous study, which loses the discriminating information. In current study, we proposed a weighting strategy with nonlinear function to combine all the correlation coefficients to enhance the performance of CORRCA method. Extensive experimental results on a benchmark dataset of thirty-five subjects  indicate that the proposed method significantly outperforms the original CORRCA method.
Revised: Correlated component analysis (CORRCA) is a novel method for frequency recognition in steady-state visual evoked potential (SSVEP) based brain-computer interface (BCI), which holds the potential to implement high-performance frequency recognition methods. The proposed framework includes two primary technique for fusing features: spatial dimension fusion (SD) and frequency dimension fusion (FD). Both SD and FD fusions are obtained using a weighted strategy with a nonlinear function. To assess our novel methods, we used the correlated component analysis (CORRCA) method to investigate the efficiency and effectiveness of the proposed framework. Experimental results were obtained from a benchmark dataset of thirty-five subjects indicate that the proposed method significantly outperforms the original CORRCA method.
Edit intent: meaning-changed
Original:  Extensive experimental results on a benchmark dataset of thirty-five subjects  indicate that the proposed method significantly outperforms the original CORRCA method. This study demonstrates that the proposed method could be a good choice for frequency recognition in SSVEP-based BCI systems .
Revised:  Extensive experimental results on a benchmark dataset of thirty-five subjects indicate that the proposed method significantly outperforms the original CORCCA method. Accordingly, the proposed framework holds promise to enhance the performance of frequency recognition methods in SSVEP-based BCI systems .
Edit intent: clarity
Original: Guth showed that given a family \mathcal{S of n g-dimensional semi-algebraic sets in R^d and an integer parameter D\geq 1 , there is a d-variate partitioning polynomial P of degree at most D , so that each connected component of R^d\setminus Z(P)
Revised: In 2015, Guth proved that if S is a collection of n g-dimensional semi-algebraic sets in R^d and an integer parameter D\geq 1 , there is a d-variate partitioning polynomial P of degree at most D , so that each connected component of R^d\setminus Z(P)
Edit intent: clarity
Original: Guth showed that given a family \mathcal{S of n g-dimensional semi-algebraic sets in R^d and an integer parameter D\geq 1 , there is a d-variate partitioning polynomial P of degree at most D , so that each connected component of R^d\setminus Z(P)
Revised: Guth showed that given a family \mathcal{S of n g-dimensional semi-algebraic sets in R^d and if D\geq 1 , there is a d-variate partitioning polynomial P of degree at most D , so that each connected component of R^d\setminus Z(P)
Edit intent: clarity
Original: Guth showed that given a family \mathcal{S of n g-dimensional semi-algebraic sets in R^d and an integer parameter D\geq 1 , there is a d-variate partitioning polynomial P of degree at most D , so that each connected component of R^d\setminus Z(P)
Revised: Guth showed that given a family \mathcal{S of n g-dimensional semi-algebraic sets in R^d and an integer parameter D\geq 1 is an integer, then there is a d-variate partitioning polynomial P of degree at most D , so that each connected component of R^d\setminus Z(P)
Edit intent: meaning-changed
Original: Guth showed that given a family \mathcal{S of n g-dimensional semi-algebraic sets in R^d and an integer parameter D\geq 1 , there is a d-variate partitioning polynomial P of degree at most D , so that each connected component of R^d\setminus Z(P)
Revised: Guth showed that given a family \mathcal{S of n g-dimensional semi-algebraic sets in R^d and an integer parameter D\geq 1 , there is a d-variate polynomial P of degree at most D , so that each connected component of R^d\setminus Z(P)
Edit intent: clarity
Original: Guth showed that given a family \mathcal{S of n g-dimensional semi-algebraic sets in R^d and an integer parameter D\geq 1 , there is a d-variate partitioning polynomial P of degree at most D , so that each connected component of R^d\setminus Z(P)
Revised: Guth showed that given a family \mathcal{S of n g-dimensional semi-algebraic sets in R^d and an integer parameter D\geq 1 , there is a d-variate partitioning polynomial P of degree at most D so that each connected component of R^d\setminus Z(P)
Edit intent: fluency