### TABLE 1 Comparison of two asymptotically equivalent forms for centering constant ~~

### Table 8. Asymptotic elapsed time for different partitioning schemes.

"... In PAGE 8: ... 6. Performance improvement Table8 depicts the asymptotic elapsed times for MIN simulation. The comparisons show that by transforming the MIN into a more modular equivalent interconnection, the message transit time can be significantly reduced.... ..."

### Table 1: Equivalence Class Counts

"... In PAGE 7: ... Letting rn be the ratio on n vertices of equivalence classes to ADGs, this produces the recursive formula rn+1 = rn - (rn-1- rn)/s. However, the numbers in Table1 show that s is not constant and itself is approximately exponentially approaching an asymptotic value of 2. Even though the following coefficients have been selected partly for their simplicity, s can nevertheless be predicted reasonably well by the equation sn = 2 + 20/3 exp(-n/2).... ..."

### Table 1: Equivalence Class Counts

2001

"... In PAGE 4: ... 3 RESULTS The first result is simply the total number of equivalence classes by number of vertices. Table1 shows these totals, along with the ratios of the numbers of classes to ADGs and the ratios of the counts of size 1 classes to the total class counts. Table 1: Equivalence Class Counts... In PAGE 4: ... Letting rn be the ratio on n vertices of equivalence classes to ADGs, this produces the recursive formula rn+1 = rn - (rn-1 - rn)/s. However, the numbers in Table1 show that s is not constant and itself is approximately exponentially approaching an asymptotic value of 2. Even though the following coefficients have been selected partly for their simplicity, s can nevertheless be predicted reasonably well by the equation sn = 2 + 20/3 exp(-n/2).... ..."

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### Table 2.1: The logical connectives

1995

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### Table 3: Equivalents Under the Tanh Transformation

"... In PAGE 13: ... (Hunter[17] solved these problems only in the asymptotic limit jXj!1.) Table3 collects the various identities which are helpful in transforming to the new coordinate z and then back again. Unfortunately, it was not possible to flnd complete explicit inner solutions at third and higher order.... ..."

### Table 1: Rejection frequencies for di erent values of ( = 1) Test statistic 1 0.95 0.9 0.8 0.5 0

"... In PAGE 14: ... Note that for r = 1 this test is asymptotically equivalent to Harris apos; (1997) test and, thus, we expect that our results apply to the latter test as well.1 Table1 reports the rejection frequencies computed from 10.000 samples generated from the model (18) { (19) with sample size T = 200.... ..."

### Table 2: The number of C-trees and of equivalence classes of C-trees for m =0;1;:::;6.

"... In PAGE 27: ... It is easy to a#0Erm the recursive formula ~ #12 0 =1; ~ #12 2m,1 = 1 2 2m,2 X j=0 ~ #12 j ~ #12 2m,j,2 + 1 2 ~ #12 m,1 ; ~ #12 2m = 1 2 2m,1 X j=0 ~ #12 j ~ #12 2m,j,1 ; m 2 N and it follows after an elementary manipulation that the generating function ~ #02#28z#29= 1 X m=0 ~ #12 m z m obeys the functional equation ~ #02#28z#29=1+ 1 2 z#5B ~ #02#28z#29#5D 2 + 1 2 z ~ #02#28z 2 #29: Neither an exact formula for f ~ #12 m g m2Z + nor an asymptotic expansion are known #5B6#5D. Yet, as can be seen from Table2 , the procedure of lumping all equivalent trees together saves a substantial proportion of computational cost. Redundancy of strictly binary trees is just one mechanism that allows us to reduce the number of commutators that need be computed.... ..."

### Table 7: RM Evaluation Test Results: XW triphones, improved duration model

### Table 1 Asymptotic properties.

1998

"... In PAGE 15: ... Such a simple example su ces to demonstrate the poorness of the asymptotic approximation. The results are given in Table1 , and it is seen that even for very large sample sizes the approximation is not good. In fact a rectangular weight function on [?1; 1] gave somewhat better results, the empirical sizes for ^ L2(M1), ^ L2(M0 1) and ^ L2(M00 1 ) being 0.... In PAGE 15: ... As in Hjellvik and Tj stheim (1995), a better nite sample t can be obtained by using a gamma distribution (or 2 distribution), but the problem of a very poor approximation to the location and scale parameters persists (cf. Table1 ). Better approximation in a spesial case using a xed experimental design have been reported by Poggi and Portier (1995).... In PAGE 17: ...1) with a = 0:5. By comparison to Table1 it is seen that the results obtained represent a vast improvement over those which could be achieved using asymptotic theory, where the size would be drastically underestimated for ^ L2(M1) and overestimated for ^ L2(M0 1) and ^ L2(M00 1 ). It is seen that ^ L0(M1) collapses when h 1:0, the other statistics seem to be quite independent of h.... In PAGE 37: ... The bandwidth is cross-validated according to Table 3, and the upper limit of the estimated order of the autoregressive t is ^ p = n=10. Table captions Table1 : The ratio between the asymptotic values given by Theorem 3.2 and simulated values for the mean and standard deviation of ^ L2(M1), ^ L2(M0 1) and ^ L2(M00 1 ), and the empirical sizes for these statistics when they have been centered by the asymptotic mean and scaled by the asymptotic standard deviation of Theorem 3.... ..."

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