### Table 1: The critical temperatures predicted by the Bethe-Peierls approximation D

"... In PAGE 4: ... Our results from the Binder parameter suggest a slightly lower value that can be explained in part as a nite D correction. In fact, a Bethe-Peierls approximation for the Heisenberg spin glass with coordination D predicts a tranisition at a critical temperature given by the equation [1]: (D ? 1) [coth(Jij=Tc) ? Tc=Jij]2 = 1 (9) In Table1 we show the solutions of this equation for di erent D values. Note that the results will depend strongly on the normalization chosen for the J0 ijs, for example if we had chosen J2 ij = 1 as usual for short range models, the Tc predicted for D = 8 would... ..."

### Table 1: F1 performance measure for various training methods on the 2-clique and 4-clique models.

2005

"... In PAGE 7: ... This sort of pa- rameter tying is necessary in a conditional model because until we observe the input x, we do not know how many output nodes there will be or what connections they will have. Table1 compares the testing performance of the differ- ent training methods on the 2-clique model (first column). First, we note that both in CF and ML training, the Bethe approximation results in better accuracy than the mean- field approximation.... ..."

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### TABLE III _____________________________________________________________________________________________ Reducible representations as supported by the BETHE program.*

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### Table 2: The critical temperatures from a linear t of the high temperature data be Tc = 0:6825 instead of Tc = 0:2413, a considerable di erence. As can be seen the Tc predicted for the range of D studied in our simulations are considerably lower than the mean eld value 0.333 which shows that the approach to the mean eld limit is slow. The mean eld spin glass susceptibility for an Heisenberg system in the paramagnetic phase can be shown to be:

"... In PAGE 5: ... From the linear ts we were able to estimate by extrapolation the critical temperatures for the di erent D studied and compare with the results of the Bethe-Peierls approximation. The results are summarized in Table2 and show a very good agreement with the analytic ones of Table 1. 4 Conclusions We have presented evidence that isotropic Heisenberg spin glasses with nite connectivities present, at low temperatures, a spin glass transition for not too small connectivities.... ..."

### Table 10: Loading and Extraction Results for the Mac Beth XML Data Set.

2002

"... In PAGE 35: ... The XML Schema has 21 different element types, no attributes, and the data set has a sum of 3,975 elements with the deepest nesting level of 6. Table10 shows some benchmark numbers and Figure 20 shows the comparison of the... ..."

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### Table 4: The shifts ( ) performed on the Bethe Ansatz variables ( ) j .

1997

### Table 2: Estimating Standard Errors with a Firm Effect Fama-MacBeth Standard Errors

"... In PAGE 15: ...o 15 percent of the OLS t-statistics when DX = D, = 0.50 (see Table 1 and 2). 14 To document the bias of the Fama-MacBeth standard error estimates, I calculate the Fama- MacBeth estimate of the slope coefficient and the standard error in each of the 5,000 simulated data sets which were used in Table 1. The results are reported in Table2 . The Fama-MacBeth estimates are consistent and as efficient as OLS (the correlation between the two is consistently above 0.... In PAGE 15: ...re consistent and as efficient as OLS (the correlation between the two is consistently above 0.99). The standard deviation of the two coefficient estimates is also the same (compare the second entry in each cell of Table 1 and 2). These results demonstrate that both OLS and Fama-MacBeth standard errors are biased downward (see Table2 ). However the Fama-MacBeth standard errors have a larger bias than the OLS standard errors.... In PAGE 15: ...acBeth standard error has a bias of 74 percent (0.738 = 1 - 0.0183/0.0699, see Table II). Moving down the diagonal of Table2 from upper left to bottom right, the true standard error increases but the standard error estimated by Fama-MacBeth actually shrinks. Remember, the estimated OLS standard errors did not change as we moved down the diagonal of Table 1.... ..."

### Table 2: Estimating Standard Errors with a Firm Effect Fama-MacBeth Standard Errors

"... In PAGE 15: ...o 15 percent of the OLS t-statistics when DX = D, = 0.50 (see Table 1 and 2). 14 MacBeth estimate of the slope coefficient and the standard error in each of the 5,000 simulated data sets which were used in Table 1. The results are reported in Table2 . The Fama-MacBeth estimates are consistent and as efficient as OLS (the correlation between the two is consistently above 0.... In PAGE 15: ...re consistent and as efficient as OLS (the correlation between the two is consistently above 0.99). The standard deviation of the two coefficient estimates is also the same (compare the second entry in each cell of Table 1 and 2). These results demonstrate that both OLS and Fama-MacBeth standard errors are biased downward (see Table2 ). However the Fama-MacBeth standard errors have a larger bias than the OLS standard errors.... In PAGE 15: ...acBeth standard error has a bias of 74 percent (0.738 = 1 - 0.0183/0.0699, see Table II). Moving down the diagonal of Table2 from upper left to bottom right, the true standard error increases but the standard error estimated by Fama-MacBeth actually shrinks. Remember, the estimated OLS standard errors did not change as we moved down the diagonal of Table 1.... ..."

### Table 4: Estimating Standard Errors with a Time Effect Fama-MacBeth Standard Errors

"... In PAGE 24: ... When there is only a time effect, the correlation of the estimated slope coefficients across years is zero and the standard errors estimated by Fama-MacBeth are unbiased (see equation 12). This is what I find in the simulation (see Table4 ). The estimated standard errors are extremely close to the true standard errors and the number of statistically significant t-statistics is close to three percent across the simulations (using a 1 percent critical value).... ..."

### Table 6: Fama-MacBeth Regressions including Characteristics Panel A: Size

"... In PAGE 29: ... Berk (1995) and Jagannathan and Wang (1998) argue that including this rm-speci c characteristic provides a natural speci cation test for any cross-sectional asset pricing model. These results are presented in Table6 . For reference, the table presents results for models which include various factors; we summarize only the main ndings from a few speci cations here.... In PAGE 29: ... Again, to form a basis of comparison, we begin by presenting the results of including rm size in the static CAPM model (11). The results of this estimation are shown in row 1 of Table6 . These results con rm the well-documented di culty posed by the inclusion of rm-speci c characteristics for the static-CAPM: the coe cient on the size variable is statistically signi cant and the risk price for the value-weighted return is now negative and statistically signi cant.... In PAGE 50: ...Table6 : This table presents estimates of cross-sectional Fama-MacBeth regressions using returns of 25 Fama-French portfolios: E[Ri;t+1] = E[R0;t] + 0 + dCi; where Ci denotes a characteristic variable. The time-series betas are computed in one multiple regression.... In PAGE 51: ...02) (-3.02) Notes for Table6 : This table presents estimates of cross-sectional Fama-MacBeth regressions using returns of 25 Fama-French portfolios: E[Ri;t+1] = E[R0;t] + 0 : The time-series betas are computed in one multiple regressions. The factors are the return of the value- weighted CRSP index (Rvw), labor income growth ( yt+1) and per capita consumption growth ( c).... ..."