wanyu/IteraTeR_full_sent huggingface dataset:
Original:   The mathematical implementation of such phenomenological postulates allows to infer quite simply a functional relationship between the mean firing-rate of the neural population and the concentration of any odorant as well as the statistical distribution of the sensitivity of any receptor neuron to any odorant across the population;
Revised:  In particular, it is assumed that the receptor neurons mean firing-rate scale monotonically with odorant intensity, and that the receptor sensitivities range widely across odorants and receptor neurons hence leading to highly distributed representations of the stimuli. The mathematical implementation of such phenomenological postulates allows to infer quite simply a functional relationship between the mean firing-rate of the neural population and the concentration of any odorant as well as the statistical distribution of the sensitivity of any receptor neuron to any odorant across the population;
Edit intent: meaning-changed
Original:   The mathematical implementation of such phenomenological postulates allows to infer quite simply a functional relationship between the mean firing-rate of the neural population and the concentration of any odorant as well as the statistical distribution of the sensitivity of any receptor neuron to any odorant across the population;
Revised:  The mathematical implementation of the phenomenological postulates allows to infer quite simply a functional relationship between the mean firing-rate of the neural population and the concentration of any odorant as well as the statistical distribution of the sensitivity of any receptor neuron to any odorant across the population;
Edit intent: clarity
Original:   The mathematical implementation of such phenomenological postulates allows to infer quite simply a functional relationship between the mean firing-rate of the neural population and the concentration of any odorant as well as the statistical distribution of the sensitivity of any receptor neuron to any odorant across the population;
Revised:  The mathematical implementation of such phenomenological postulates allows for inferring explicit functional relationships between some measurable quantities. It results that both the dependence of the mean firing-rate of the neural population and the concentration of any odorant as well as the statistical distribution of the sensitivity of any receptor neuron to any odorant across the population;
Edit intent: meaning-changed
Original:   The mathematical implementation of such phenomenological postulates allows to infer quite simply a functional relationship between the mean firing-rate of the neural population and the concentration of any odorant as well as the statistical distribution of the sensitivity of any receptor neuron to any odorant across the population;
Revised:  The mathematical implementation of such phenomenological postulates allows to infer quite simply a functional relationship between the mean firing-rate on odorant concentration and the statistical distribution of the sensitivity of any receptor neuron to any odorant across the population;
Edit intent: clarity
Original:   The mathematical implementation of such phenomenological postulates allows to infer quite simply a functional relationship between the mean firing-rate of the neural population and the concentration of any odorant as well as the statistical distribution of the sensitivity of any receptor neuron to any odorant across the population; both of them turn out to be power-laws and an arithmetic, testable relationship between the respective exponents naturally appears .
Revised:  The mathematical implementation of such phenomenological postulates allows to infer quite simply a functional relationship between the mean firing-rate of the neural population and the concentration of any odorant as well as the statistical distribution of receptor sensitivity across the neuronal population are power-laws and an arithmetic, testable relationship between the respective exponents naturally appears .
Edit intent: coherence
Original:  In order to compare quantitatively the prediction of power-law dependence of population mean firing-rate on odorant concentration, a probabilistic model is created to extract information from data available in the experimental literature which, inter alia, allows to pool together several data-sets and hence increase statistical accuracy .
Revised:  In order to test quantitatively the prediction of power-law dependence of population mean firing-rate on odorant concentration, a probabilistic model is created to extract information from data available in the experimental literature which, inter alia, allows to pool together several data-sets and hence increase statistical accuracy .
Edit intent: clarity
Original:  In order to compare quantitatively the prediction of power-law dependence of population mean firing-rate on odorant concentration, a probabilistic model is created to extract information from data available in the experimental literature which, inter alia, allows to pool together several data-sets and hence increase statistical accuracy .
Revised:  In order to compare quantitatively the prediction of power-law dependence of population mean firing-rate on odorant concentration, a probabilistic model is created to extract information from data available in the experimental literature .
Edit intent: coherence
Original:  The probabilistic model results to be accurate, thus confirming the theoretical prediction of a power-law dependence on odorant concentration. The experimental data available about the distribution of sensitivities also agree with the other predictions, though they are not statistically sufficient for a very stringent verification. The theory also suggests a possible explanation for the range of values of the exponent of the sensitivity power-law found in experiments.
Revised:  CONTINUES
Edit intent: coherence
Original:  By making use of the Stochastic Hybrid System (SHS) method, we provide a derivation of the average Age of Information of a system of two parallel servers (with and without buffer capabilities) and compare the result with that of a single queue.
Revised:  By making use of the Stochastic Hybrid System (SHS) method, we provide a derivation of the average AoI of a system of two parallel servers (with and without buffer capabilities) and compare the result with that of a single queue.
Edit intent: clarity
Original:  By making use of the Stochastic Hybrid System (SHS) method, we provide a derivation of the average Age of Information of a system of two parallel servers (with and without buffer capabilities) and compare the result with that of a single queue.
Revised:  By making use of the Stochastic Hybrid System (SHS) method, we provide a derivation of the average Age of Information of a system of two parallel queues (with and without buffer capabilities) and compare the result with that of a single queue.
Edit intent: clarity
Original:  By making use of the Stochastic Hybrid System (SHS) method, we provide a derivation of the average Age of Information of a system of two parallel servers (with and without buffer capabilities) and compare the result with that of a single queue.
Revised:  By making use of the Stochastic Hybrid System (SHS) method, we provide a derivation of the average Age of Information of a system of two parallel servers (with and without buffer capabilities) and compare the results with those of a single queue.
Edit intent: fluency
Original:  We therefore provide an upper bound of the average Age of Information in a parallel server system of an arbitrary number of M/M/1/(N+1) queues and  its tightness in various regimes.
Revised:  We therefore provide an upper bound of the average Age of Information in a parallel server system of an arbitrary number of M/M/1/(N+1) queues and show its tightness in various regimes.
Edit intent: coherence
Original:  This upper bound allows providing a tight approximation of the Age of Information with a very low complexity  .
Revised:  This upper bound allows providing a tight approximation of the Age of Information with a very low complexity . We then provide a game framework that allows each source to determine its best probabilistic routing decision. By using Mean Field Games, we provide an analysis of the routing game framework, propose an efficient iterative method to find the routing decision of each source and prove its convergence to the desired equilibrium .
Edit intent: meaning-changed
Original:  One way to analyse the scaling properties of time series is through the estimation of scaling exponents. These exponents are recognized as being valuable measures to discriminate between random, persistent, and anti-persistent behaviours in time series.
Revised:  One way to analyse the scaling properties of time series is through the estimation of their scaling exponents, that are recognized as being valuable measures to discriminate between random, persistent, and anti-persistent behaviours in time series.
Edit intent: clarity
Original:  In the literature, several methods have been proposed to study the multiscaling property and in this paper we use the generalized Hurst exponent (GHE) . On the base of this methodology, we propose a novel statistical procedure  to robustly estimate and test the multiscaling property and we name it RNSGHE.
Revised:  In the literature, several methods have been proposed to study the multiscaling property and in this paper we use the generalized Hurst exponent (GHE) tool and we propose a novel statistical procedure to robustly estimate and test the multiscaling property and we name it RNSGHE.
Edit intent: clarity
Original:  On the base of this methodology, we propose a novel statistical procedure  to robustly estimate and test the multiscaling property and we name it RNSGHE.
Revised:  On the base of this methodology, we propose a novel statistical procedure based on GHE which we name Relative Normalized and Standardized Generalized Hurst Exponent (RNSGHE). This method is used to robustly estimate and test the multiscaling property and we name it RNSGHE.
Edit intent: meaning-changed
Original:  On the base of this methodology, we propose a novel statistical procedure  to robustly estimate and test the multiscaling property and we name it RNSGHE. This methodology , together with a combination of t-tests and F-tests to discriminated between real and spurious scaling.
Revised:  On the base of this methodology, we propose a novel statistical procedure to robustly estimate and test the multiscaling property and , together with a combination of t-tests and F-tests to discriminated between real and spurious scaling.
Edit intent: coherence
Original:  We show that by using this statistical procedure in combination with the robustly estimated multiscaling exponents, the one year forecasted MSVaR mimics the VaR on the annual data for the majority of the stocks analysed .
Revised:  We show that by using this statistical procedure in combination with the robustly estimated multiscaling exponents, the one year forecasted MSVaR mimics the VaR on the annual data for the majority of the stocks analyzed .
Edit intent: fluency
Original: We give the first efficient algorithm for the problem of list-decodable subspace recovery . Our algorithm takes input n samples \alpha n (  \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r }  with a isotropic rank r covariance \Pi_* (the } and the rest are arbitrary, potentially adversarial outliers.
Revised: We give the first efficient algorithm for the problem of list-decodable subspace recovery , the input is a collection of n points \alpha n ( \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r } with a isotropic rank r covariance \Pi_* (the } and the rest are arbitrary, potentially adversarial outliers.
Edit intent: clarity
Original:  Our algorithm takes input n samples \alpha n (  \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r }  with a isotropic rank r covariance \Pi_* (the } and the rest are arbitrary, potentially adversarial outliers.
Revised:  Our algorithm takes input n samples \alpha n ( for some \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r } with a isotropic rank r covariance \Pi_* (the } and the rest are arbitrary, potentially adversarial outliers.
Edit intent: meaning-changed
Original:  Our algorithm takes input n samples \alpha n (  \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r }  with a isotropic rank r covariance \Pi_* (the } and the rest are arbitrary, potentially adversarial outliers.
Revised:  Our algorithm takes input n samples \alpha n ( \alpha \ll 1/2) of which are drawn i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r } with a isotropic rank r covariance \Pi_* (the } and the rest are arbitrary, potentially adversarial outliers.
Edit intent: clarity
Original:  Our algorithm takes input n samples \alpha n (  \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r }  with a isotropic rank r covariance \Pi_* (the } and the rest are arbitrary, potentially adversarial outliers.
Revised:  Our algorithm takes input n samples \alpha n ( \alpha \ll 1/2) are generated i.i.d. from (0,\Sigma_*) on R^d with covariance \Sigma_* of rank r } with a isotropic rank r covariance \Pi_* (the } and the rest are arbitrary, potentially adversarial outliers.
Edit intent: meaning-changed
Original:  Our algorithm takes input n samples \alpha n (  \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r }  with a isotropic rank r covariance \Pi_* (the } and the rest are arbitrary, potentially adversarial outliers.
Revised:  Our algorithm takes input n samples \alpha n ( \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r } a distribution \mathcal{D with a isotropic rank r covariance \Pi_* (the } and the rest are arbitrary, potentially adversarial outliers.
Edit intent: meaning-changed
Original:  Our algorithm takes input n samples \alpha n (  \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r }  with a isotropic rank r covariance \Pi_* (the } and the rest are arbitrary, potentially adversarial outliers.
Revised:  Our algorithm takes input n samples \alpha n ( \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r } with a isotropic rank r covariance \Pi_* (the }inliers and the rest are arbitrary, potentially adversarial outliers.
Edit intent: fluency
Original:  Our algorithm takes input n samples \alpha n (  \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r }  with a isotropic rank r covariance \Pi_* (the } and the rest are arbitrary, potentially adversarial outliers.
Revised:  Our algorithm takes input n samples \alpha n ( \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r } with a isotropic rank r covariance \Pi_* (the }) and the rest are arbitrary, potentially adversarial outliers.
Edit intent: fluency
Original:  Our algorithm takes input n samples \alpha n (  \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r }  with a isotropic rank r covariance \Pi_* (the } and the rest are arbitrary, potentially adversarial outliers.
Revised:  Our algorithm takes input n samples \alpha n ( \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r } with a isotropic rank r covariance \Pi_* (the } and the rest are arbitrary, potential adversarial outliers.
Edit intent: fluency
Original:  It outputs a list of O(1/\alpha) projection matrices guaranteed to contain a projection matrix%DIFDELCMD < \Pisuch %%% that\hat{\Pi}  satisfies certifiable anti-concentration.
Revised:  The goal is to recover a O(1/\alpha) projection matrices guaranteed to contain a projection matrix%DIFDELCMD < \Pisuch %%% that\hat{\Pi} satisfies certifiable anti-concentration.
Edit intent: clarity
Original:  It outputs a list of O(1/\alpha) projection matrices guaranteed to contain a projection matrix%DIFDELCMD < \Pisuch %%% that\hat{\Pi}  satisfies certifiable anti-concentration.
Revised:  It outputs a list of O(1/\alpha) %DIFDELCMD < \Pisuch %%% that\hat{\Pi} satisfies certifiable anti-concentration.
Edit intent: clarity
Original:  It outputs a list of O(1/\alpha) projection matrices guaranteed to contain a projection matrix%DIFDELCMD < \Pisuch %%% that\hat{\Pi}  satisfies certifiable anti-concentration.
Revised:  It outputs a list of O(1/\alpha) projection matrices guaranteed to contain a projection matrix%DIFDELCMD < \Pisuch %%% size list of candidate covariances that contains a\hat{\Pi} satisfies certifiable anti-concentration.
Edit intent: meaning-changed
Original:  It outputs a list of O(1/\alpha) projection matrices guaranteed to contain a projection matrix%DIFDELCMD < \Pisuch %%% that\hat{\Pi}  satisfies certifiable anti-concentration.
Revised:  It outputs a list of O(1/\alpha) projection matrices guaranteed to contain a projection matrix%DIFDELCMD < \Pisuch %%% that\hat{\Pi} close to \Pi_*. Two recent independent works (Raghavendra-Yau, Bakshi-Kothari (2020)) gave algorithms for this problem that work whenever \mathcal{D satisfies certifiable anti-concentration.
Edit intent: meaning-changed
Original:  The running time of both these algorithms, however, is d^{\Omega(1/\alpha^4)} and the error bounds on } \|\Pi-\Pi_*\|_F ^2 = \kappa^4 \log (r )%DIFDELCMD < \tilde{O}%%% (\emph{  1/ \alpha^2), where%DIFDELCMD < \tilde{O} %%% hides polylogarithmic factors in 1/ \alpha .
Revised:  The running time of both these algorithms, however, is d^{\Omega(1/\alpha^4)} and the error bounds on } \|\Pi-\Pi_*\|_F %DIFDELCMD < \tilde{O}%%% (\emph{ 1/ \alpha^2), where%DIFDELCMD < \tilde{O} %%% hides polylogarithmic factors in 1/ \alpha .
Edit intent: coherence
Original:  The running time of both these algorithms, however, is d^{\Omega(1/\alpha^4)} and the error bounds on } \|\Pi-\Pi_*\|_F ^2 = \kappa^4 \log (r )%DIFDELCMD < \tilde{O}%%% (\emph{  1/ \alpha^2), where%DIFDELCMD < \tilde{O} %%% hides polylogarithmic factors in 1/ \alpha .
Revised:  The running time of both these algorithms, however, is d^{\Omega(1/\alpha^4)} and the error bounds on } \|\Pi-\Pi_*\|_F ^2 = \kappa^4 \log (r )%DIFDELCMD < \tilde{O}%%% grow with r (which can be \Omega(d)). In this work, we improve on these results on all three fronts:\emph{ 1/ \alpha^2), where%DIFDELCMD < \tilde{O} %%% hides polylogarithmic factors in 1/ \alpha .
Edit intent: meaning-changed
Original:  The running time of both these algorithms, however, is d^{\Omega(1/\alpha^4)} and the error bounds on } \|\Pi-\Pi_*\|_F ^2 = \kappa^4 \log (r )%DIFDELCMD < \tilde{O}%%% (\emph{  1/ \alpha^2), where%DIFDELCMD < \tilde{O} %%% hides polylogarithmic factors in 1/ \alpha .
Revised:  The running time of both these algorithms, however, is d^{\Omega(1/\alpha^4)} and the error bounds on } \|\Pi-\Pi_*\|_F ^2 = \kappa^4 \log (r )%DIFDELCMD < \tilde{O}%%% (\emph{dimension-independent 1/ \alpha^2), where%DIFDELCMD < \tilde{O} %%% hides polylogarithmic factors in 1/ \alpha .
Edit intent: meaning-changed
Original:  The running time of both these algorithms, however, is d^{\Omega(1/\alpha^4)} and the error bounds on } \|\Pi-\Pi_*\|_F ^2 = \kappa^4 \log (r )%DIFDELCMD < \tilde{O}%%% (\emph{  1/ \alpha^2), where%DIFDELCMD < \tilde{O} %%% hides polylogarithmic factors in 1/ \alpha .
Revised:  The running time of both these algorithms, however, is d^{\Omega(1/\alpha^4)} and the error bounds on } \|\Pi-\Pi_*\|_F ^2 = \kappa^4 \log (r )%DIFDELCMD < \tilde{O}%%% (\emph{ error via a faster fixed-polynomial running time under less restrictive distributional assumptions. Specifically, we give a poly( 1/ \alpha^2), where%DIFDELCMD < \tilde{O} %%% hides polylogarithmic factors in 1/ \alpha .
Edit intent: meaning-changed
Original:  The running time of both these algorithms, however, is d^{\Omega(1/\alpha^4)} and the error bounds on } \|\Pi-\Pi_*\|_F ^2 = \kappa^4 \log (r )%DIFDELCMD < \tilde{O}%%% (\emph{  1/ \alpha^2), where%DIFDELCMD < \tilde{O} %%% hides polylogarithmic factors in 1/ \alpha .
Revised:  The running time of both these algorithms, however, is d^{\Omega(1/\alpha^4)} and the error bounds on } \|\Pi-\Pi_*\|_F ^2 = \kappa^4 \log (r )%DIFDELCMD < \tilde{O}%%% (\emph{ 1/ %DIFDELCMD < \tilde{O} %%% hides polylogarithmic factors in 1/ \alpha .
Edit intent: coherence
Original:  The running time of both these algorithms, however, is d^{\Omega(1/\alpha^4)} and the error bounds on } \|\Pi-\Pi_*\|_F ^2 = \kappa^4 \log (r )%DIFDELCMD < \tilde{O}%%% (\emph{  1/ \alpha^2), where%DIFDELCMD < \tilde{O} %%% hides polylogarithmic factors in 1/ \alpha .
Revised:  The running time of both these algorithms, however, is d^{\Omega(1/\alpha^4)} and the error bounds on } \|\Pi-\Pi_*\|_F ^2 = \kappa^4 \log (r )%DIFDELCMD < \tilde{O}%%% (\emph{ 1/ \alpha^2), where%DIFDELCMD < \tilde{O} %%% \alpha .
Edit intent: meaning-changed
Original:  The running time of both these algorithms, however, is d^{\Omega(1/\alpha^4)} and the error bounds on } \|\Pi-\Pi_*\|_F ^2 = \kappa^4 \log (r )%DIFDELCMD < \tilde{O}%%% (\emph{  1/ \alpha^2), where%DIFDELCMD < \tilde{O} %%% hides polylogarithmic factors in 1/ \alpha . Here, \Pi_* is the projection matrix to the range space of \Sigma_*. The algorithm needs n=d ^{ \log ( r \kappa ) %DIFDELCMD < \tilde{O}%%% (\hat{\Pi} \hat{\Pi}  1/ \alpha^2) samples and runs in time n^{\log (r \kappa) \tilde{O(1/\alpha^4)} time where \kappa is the ratio of the largest to smallest non-zero eigenvalues of \Sigma_*.
Revised:  The running time of both these algorithms, however, is d^{\Omega(1/\alpha^4)} and the error bounds on } \|\Pi-\Pi_*\|_F ^2 = \kappa^4 \log (r )%DIFDELCMD < \tilde{O}%%% (\emph{ 1/ \alpha^2), where%DIFDELCMD < \tilde{O} %%% hides polylogarithmic factors in 1/ \alpha ) d ^{ \log ( r \kappa ) %DIFDELCMD < \tilde{O}%%% (\hat{\Pi} \hat{\Pi} 1/ \alpha^2) samples and runs in time n^{\log (r \kappa) \tilde{O(1/\alpha^4)} time where \kappa is the ratio of the largest to smallest non-zero eigenvalues of \Sigma_*.
Edit intent: meaning-changed
Original:  The algorithm needs n=d ^{ \log ( r \kappa ) %DIFDELCMD < \tilde{O}%%% (\hat{\Pi} \hat{\Pi}  1/ \alpha^2) samples and runs in time n^{\log (r \kappa) \tilde{O(1/\alpha^4)} time where \kappa is the ratio of the largest to smallest non-zero eigenvalues of \Sigma_*.
Revised:  The algorithm needs n=d ^{ O ( r \kappa ) %DIFDELCMD < \tilde{O}%%% (\hat{\Pi} \hat{\Pi} 1/ \alpha^2) samples and runs in time n^{\log (r \kappa) \tilde{O(1/\alpha^4)} time where \kappa is the ratio of the largest to smallest non-zero eigenvalues of \Sigma_*.
Edit intent: fluency
Original:  The algorithm needs n=d ^{ \log ( r \kappa ) %DIFDELCMD < \tilde{O}%%% (\hat{\Pi} \hat{\Pi}  1/ \alpha^2) samples and runs in time n^{\log (r \kappa) \tilde{O(1/\alpha^4)} time where \kappa is the ratio of the largest to smallest non-zero eigenvalues of \Sigma_*.
Revised:  The algorithm needs n=d ^{ \log ( 1 ) %DIFDELCMD < \tilde{O}%%% (\hat{\Pi} \hat{\Pi} 1/ \alpha^2) samples and runs in time n^{\log (r \kappa) \tilde{O(1/\alpha^4)} time where \kappa is the ratio of the largest to smallest non-zero eigenvalues of \Sigma_*.
Edit intent: meaning-changed