wanyu/IteraTeR_full_sent huggingface dataset:
Original:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Revised:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %%% %DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Edit intent: coherence
Original:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Revised:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %%% where N_e(%DIFDELCMD < \bX%%% %DIFDELCMD < \bX%%% , \mu_e is its chemical potential;
Edit intent: meaning-changed
Original:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% , \mu_e is its chemical potential; the index i, 1%DIFDELCMD < \le %%% i%DIFDELCMD < \le %%% H, is the hydrophobicity classification of atoms.
Revised:  The formula has two versions, the chemical balance version is: equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = \mu_eN_e(%DIFDELCMD < \bX%%% ) + \sum_{i=1^H \mu_i N_i(}%DIFDELCMD < \bX%%% ), equation*%DIFDELCMD < } %%% where N_e(%DIFDELCMD < \bX%%% ) is the mean number of electrons in the space included by the first hydration shell of%DIFDELCMD < \bX%%% %DIFDELCMD < \le %%% i%DIFDELCMD < \le %%% H, is the hydrophobicity classification of atoms.
Edit intent: meaning-changed
Original:  the index i, 1%DIFDELCMD < \le %%% i%DIFDELCMD < \le %%% H, is the hydrophobicity classification of atoms. N_i(%DIFDELCMD < \bX%%% ) is the mean number of water molecules in the first hydration layer that directly contact to the atoms with the hydrophobicity degree i;
Revised:  the index i, 1%DIFDELCMD < \le %%% i%DIFDELCMD < \le %%% %DIFDELCMD < \bX%%% ) is the mean number of water molecules in the first hydration layer that directly contact to the atoms with the hydrophobicity degree i;
Edit intent: clarity
Original:  N_i(%DIFDELCMD < \bX%%% ) is the mean number of water molecules in the first hydration layer that directly contact to the atoms with the hydrophobicity degree i; \mu_i is the chemical potential. Label all atoms of hydrophobicity degree i by H_i and let M_\bX be the molecular surface for the conformation%DIFDELCMD < \bX%%% , defining M_{\bX_i as the set of points in M_\bX that are closer to atoms in H_i than any atoms in H_j, j }%DIFDELCMD < \ne %%% i. Then the geometric version of G(%DIFDELCMD < \bX%%% ) resembles to well-known surface area models , plus a volume term:
Revised:  N_i(%DIFDELCMD < \bX%%% %DIFDELCMD < \bX%%% , defining M_{\bX_i as the set of points in M_\bX that are closer to atoms in H_i than any atoms in H_j, j }%DIFDELCMD < \ne %%% i. Then the geometric version of G(%DIFDELCMD < \bX%%% ) resembles to well-known surface area models , plus a volume term:
Edit intent: coherence
Original:  Label all atoms of hydrophobicity degree i by H_i and let M_\bX be the molecular surface for the conformation%DIFDELCMD < \bX%%% , defining M_{\bX_i as the set of points in M_\bX that are closer to atoms in H_i than any atoms in H_j, j }%DIFDELCMD < \ne %%% i. Then the geometric version of G(%DIFDELCMD < \bX%%% ) resembles to well-known surface area models , plus a volume term:
Revised:  Label all atoms of hydrophobicity degree i by H_i and let M_\bX be the molecular surface for the conformation%DIFDELCMD < \bX%%% as the set of points in M_\bX that are closer to atoms in H_i than any atoms in H_j, j }%DIFDELCMD < \ne %%% i. Then the geometric version of G(%DIFDELCMD < \bX%%% ) resembles to well-known surface area models , plus a volume term:
Edit intent: clarity
Original:  Label all atoms of hydrophobicity degree i by H_i and let M_\bX be the molecular surface for the conformation%DIFDELCMD < \bX%%% , defining M_{\bX_i as the set of points in M_\bX that are closer to atoms in H_i than any atoms in H_j, j }%DIFDELCMD < \ne %%% i. Then the geometric version of G(%DIFDELCMD < \bX%%% ) resembles to well-known surface area models , plus a volume term:
Revised:  Label all atoms of hydrophobicity degree i by H_i and let M_\bX be the molecular surface for the conformation%DIFDELCMD < \bX%%% , defining M_{\bX_i as the set of points in M_\bX that are closer to atoms in H_i than any atoms in H_j, j }%DIFDELCMD < \ne %%% %DIFDELCMD < \bX%%% ) resembles to well-known surface area models , plus a volume term:
Edit intent: meaning-changed
Original:  Label all atoms of hydrophobicity degree i by H_i and let M_\bX be the molecular surface for the conformation%DIFDELCMD < \bX%%% , defining M_{\bX_i as the set of points in M_\bX that are closer to atoms in H_i than any atoms in H_j, j }%DIFDELCMD < \ne %%% i. Then the geometric version of G(%DIFDELCMD < \bX%%% ) resembles to well-known surface area models , plus a volume term:
Revised:  Label all atoms of hydrophobicity degree i by H_i and let M_\bX be the molecular surface for the conformation%DIFDELCMD < \bX%%% , defining M_{\bX_i as the set of points in M_\bX that are closer to atoms in H_i than any atoms in H_j, j }%DIFDELCMD < \ne %%% i. Then the geometric version of G(%DIFDELCMD < \bX%%% For simplicity, only monomeric self folding globular proteins are covered. We point out some immediate applications of the formula. We show that the formula explains the observed phenomena very well. It gives a unified explanation to both folding and denaturation; it explains why hydrophobic effect is the driving force of protein folding and clarifies the role played by hydrogen bonding; it explains the successes and deficients of various surface area models , plus a volume term:
Edit intent: meaning-changed
Original:  Label all atoms of hydrophobicity degree i by H_i and let M_\bX be the molecular surface for the conformation%DIFDELCMD < \bX%%% , defining M_{\bX_i as the set of points in M_\bX that are closer to atoms in H_i than any atoms in H_j, j }%DIFDELCMD < \ne %%% i. Then the geometric version of G(%DIFDELCMD < \bX%%% ) resembles to well-known surface area models , plus a volume term:
Revised:  Label all atoms of hydrophobicity degree i by H_i and let M_\bX be the molecular surface for the conformation%DIFDELCMD < \bX%%% , defining M_{\bX_i as the set of points in M_\bX that are closer to atoms in H_i than any atoms in H_j, j }%DIFDELCMD < \ne %%% i. Then the geometric version of G(%DIFDELCMD < \bX%%% ) resembles to well-known surface area models 
Edit intent: meaning-changed
Original:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%%  ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi  .
Revised:  %DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi .
Edit intent: fluency
Original:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%%  ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi  .
Revised:  equation*%DIFDELCMD < } %%% %DIFDELCMD < \bX%%% ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi .
Edit intent: coherence
Original:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%%  ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi  .
Revised:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% . The formula also gives a clear kinetic force of the folding: Fi(X ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi .
Edit intent: meaning-changed
Original:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%%  ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi  .
Revised:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = ^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi .
Edit intent: coherence
Original:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%%  ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi  .
Revised:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi .
Edit intent: meaning-changed
Original:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%%  ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi  .
Revised:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, %DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi .
Edit intent: fluency
Original:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%%  ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi  .
Revised:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% ) are the areas of M_\bX and M_{\bX_i}} \nablaxi .
Edit intent: meaning-changed
Original:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%%  ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi  .
Revised:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} -\nablaxi .
Edit intent: coherence
Original:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%%  ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi  .
Revised:  equation*%DIFDELCMD < } %%% G(%DIFDELCMD < \bX%%% ) = a\mu_e V(\Omega_\bX)+ ad_w\mu_eA(M_\bX) + \sum_{i=1^H\nu_i \mu_i A(M_{\bX_i}), }%DIFDELCMD < \quad %%% a , \nu_i > 0, equation*%DIFDELCMD < } %%% where V(\Omega_\bX) is the volume of the domain \Omega_\bX enclosed by M_\bX, d_w is the diameter of a water molecule, and A(M_\bX) and A(M_{\bX_i) are the areas of M_\bX and M_{\bX_i}} \nablaxi G(X). This also gives a natural way to perform the ab initio prediction of protein structure, minimizing G(X) by Newton's fastest desciending method .
Edit intent: coherence
Original:  However, derivative data is a set of conditional expectations that are already observed in the market, so rather than use filtering techniques we compute animplied distribution by inverting the market's option prices. Robustness is an issue when model parameters are probably unknown, but isn't crippling in practical settings because the data is sufficiently imprecise and prevents us from reducing the fitting error down to levels where parameter uncertainty will show .
Revised:  However, derivative data is a set of conditional expectations that are already observed in the market, so rather than use filtering techniques we compute animplied distribution and which can be used as input to an inverse problem whose solution is an implied conditional density on volatility. Our analysis relies on a specification of the martingale change of measure, which we refer to as .
Edit intent: meaning-changed
Original:  Robustness is an issue when model parameters are probably unknown, but isn't crippling in practical settings because the data is sufficiently imprecise and prevents us from reducing the fitting error down to levels where parameter uncertainty will show .
Revised:  Robustness is an issue when model parameters are probably unknown, but isn't crippling in practical settings because the data is sufficiently imprecise and prevents us from reducing the fitting error down to levels where parameter uncertainty will showseparability .
Edit intent: clarity
Original:  Robustness is an issue when model parameters are probably unknown, but isn't crippling in practical settings because the data is sufficiently imprecise and prevents us from reducing the fitting error down to levels where parameter uncertainty will show .
Revised:  Robustness is an issue when model parameters are probably unknown, but isn't crippling in practical settings because the data is sufficiently imprecise and prevents us from reducing the fitting error down to levels where parameter uncertainty will show. This specification has a multiplicative component that behaves like a risk premium on volatility uncertainty in the market .
Edit intent: meaning-changed
Original:  When applied to SPX  data, the estimated model and implied distributions produce variance swap rates that are consistent with the VIX , and also pick up some of the monthly effects that occur from option expiration.
Revised:  When applied to SPX data, the estimated model and implied distributions produce variance swap rates that are consistent with the VIX volatility index. The implied densities are relatively stable over time and pick up some of the monthly effects that occur from option expiration.
Edit intent: meaning-changed
Original:  When applied to SPX  data, the estimated model and implied distributions produce variance swap rates that are consistent with the VIX , and also pick up some of the monthly effects that occur from option expiration. We find that parsimony of the Heston model is beneficial because we are able to decipher behavior in estimated parameters and implied measures, whereas the richer Heston model with jumps produces a better fit but also has implied behavior that is less revealing .
Revised:  When applied to SPX data, the estimated model and implied distributions produce variance swap rates that are consistent with the VIX , and also pick up some of the monthly effects that occur due to the options' expiration, indicating that the volatility-uncertainty premium could experience cyclic effects due to the maturity date of the options .
Edit intent: meaning-changed
Original: The aim of this paper is twofold: to provide a theoretical framework and to give further empirical support to Shiller's test of the appropriateness of prices in the stock market based on the Cyclically Adjusted Price Earnings (CAPE) ratio.
Revised: We present a simple dynamical model of stock index returns which is grounded on the ability of the Cyclically Adjusted Price Earnings (CAPE) ratio.
Edit intent: clarity
Original: The aim of this paper is twofold: to provide a theoretical framework and to give further empirical support to Shiller's test of the appropriateness of prices in the stock market based on the Cyclically Adjusted Price Earnings (CAPE) ratio.
Revised: The aim of this paper is twofold: to provide a theoretical framework and to give further empirical support to Shiller's test of the appropriateness of prices in the stock market based on the Cyclically Adjusted Price Earning (CAPE) ratio.
Edit intent: fluency
Original: The aim of this paper is twofold: to provide a theoretical framework and to give further empirical support to Shiller's test of the appropriateness of prices in the stock market based on the Cyclically Adjusted Price Earnings (CAPE) ratio. We devote the first part of the paper to the empirical analysis and we show that the CAPE is a powerful predictor of future long run performances of the market not only for the U. S. but also for countries such as Belgium, France, Germany, Japan, the Netherlands, Norway, Sweden and Switzerland.
Revised: The aim of this paper is twofold: to provide a theoretical framework and to give further empirical support to Shiller's test of the appropriateness of prices in the stock market based on the Cyclically Adjusted Price Earnings (CAPE) valuation ratio devised by Robert Shiller to predict long-horizon performances of the market not only for the U. S. but also for countries such as Belgium, France, Germany, Japan, the Netherlands, Norway, Sweden and Switzerland.
Edit intent: clarity
Original:  We devote the first part of the paper to the empirical analysis and we show that the CAPE is a powerful predictor of future long run performances of the market not only for the U. S. but also for countries such as Belgium, France, Germany, Japan, the Netherlands, Norway, Sweden and Switzerland. We show four relevant empirical facts: i) the striking ability of the logarithmic averaged earning over price ratio to predict returns of the index, ii) how this evidence increases switching from returns to gross returns, iii) moving over different time horizons, the regression coefficients are constant in a statistically robust way, and iv) the poorness of the prediction when the precursor is adjusted with long term interest rate. In the second part we provide a theoretical justification of the empirical observations. Indeed we propose a simple model of the price dynamics in which the return growth depends on three components: a ) a momentum component, naturally justified in terms of agents' belief that expected returns are higher in bullish markets than in bearish ones ;
Revised:  We devote the first part of the paper to the empirical analysis and we show that the CAPE is a powerful predictor of future long run performances of the market . More precisely, we discuss a discrete time dynamics in which the return growth depends on three components: a ) a momentum component, naturally justified in terms of agents' belief that expected returns are higher in bullish markets than in bearish ones ;
Edit intent: coherence
Original:  Indeed we propose a simple model of the price dynamics in which the return growth depends on three components: a ) a momentum component, naturally justified in terms of agents' belief that expected returns are higher in bullish markets than in bearish ones ;
Revised:  Indeed we propose a simple model of the price dynamics in which the return growth depends on three components: i ) a momentum component, naturally justified in terms of agents' belief that expected returns are higher in bullish markets than in bearish ones ;
Edit intent: meaning-changed
Original:  Indeed we propose a simple model of the price dynamics in which the return growth depends on three components: a ) a momentum component, naturally justified in terms of agents' belief that expected returns are higher in bullish markets than in bearish ones ; b ) a fundamental component proportional to the log earnings over price ratio at time zero  , from which the actual stock price may deviate as an effect of random external disturbances, and c ) a driving component ensuring the diffusive behaviour of stock prices.
Revised:  Indeed we propose a simple model of the price dynamics in which the return growth depends on three components: a ) a momentum component, naturally justified in terms of agents' belief that expected returns are higher in bullish markets than in bearish ones , ii ) a fundamental component proportional to the log earnings over price ratio at time zero , from which the actual stock price may deviate as an effect of random external disturbances, and c ) a driving component ensuring the diffusive behaviour of stock prices.
Edit intent: fluency