### Table 1: Extended statistical analysis of FRITZ 6 self-play results.

2001

"... In PAGE 5: ... Personally, I have known about and done these exact calculations since the very start of my self-play research. In addition, I privately communicated the trinomial formula for a11a18a12a19a14a17a16 and the exact W / D / L results from Table1 to some interested people in mid-2001. They all agreed that the W / D / L calculations do actually not lead to a much better characterization of the diminishing- returns phenomenon than the less exact binomial ones.... In PAGE 5: ... They all agreed that the W / D / L calculations do actually not lead to a much better characterization of the diminishing- returns phenomenon than the less exact binomial ones. Despite yielding tighter confidence bounds for the a8a60a14 s as shown in Table1 , the W / D / L analysis still does not allow for any meaningful confident quantification of the decreases in winning probability for most of the iteration depths covered by the experiment. 3.... ..."

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### Table 1. Scaling exponents p of the pth order velocity structure functions mea- sured in a wind tunnel turbulence(1) (Anselmet et al., 1984), in a wake turbulence(2) (Benzi et al., 1994), in a jet turbulence(3) (transverse velocity structure function) (Noullez et al. , 1996), in a low temperature helium experiment(4) (Belin et al. 1996), and in an isotropic Navier-Stokes turbulence simulation(5) (Cao, Chen amp; She, 1996). The SL model reads p = p=9 + 2(1 ? (2=3)p=3). Secondly, the Extended Self-Similarity property in turbulence (Benzi et

"... In PAGE 10: ... In this regard, we like to make the following remarks. First, the scaling exponents of the longitudinal velocity structure functions in a far- eld of fully developed turbulent open ow have been measured in several ow environments, and the results are generally consistent (see Table1 ). In other words, these exper- imental values are robust and stable.... In PAGE 11: ... Although the mechanism is not yet clear, the fact that it is a useful property in measur- ing scalings which leads no detectable distortion of the measured value is widely accepted. So the reported values in Table1 are quite reliable. The good agreement can hardly attributed to pure coincidence.... ..."

### Table 1: Self capacitances in pF of the cube and the CPU time in sec.

1996

"... In PAGE 5: ... The cube computed is extended along one direction z. Table1 shows the results(self capacitance of the cube varying with the extended edge z) of GIMEI compared with those of FASTCAP as well as the CPU time of the two pro- grams run on Sun Sparc 20 workstation. From the table, one can clearly see that in general, GIMEI is generally an order of magnitude faster and uses much less memory than FASTCAP with the di erence of less than 1%.... ..."

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### Table 8: Number of skills modified for different numbers of driving laws in the original and extended formalism.

"... In PAGE 5: ... Thus, we varied the number of laws changed in the domain and recorded the number of skills that we needed to revise in both frameworks. Table8 presents the results from this experiment, which reveal that there was no need to modify the skills in the ex- Table 6: Skills for the driving domain with two ordered laws in the original formalism. ((at-address ?self?ad ?st) :percepts ((self ?self) (street ?st)) :start ((address-behind ?self ?ad ?st)) :requires ((not-hitting-pedestrians ?self) (at-desired-speed ?self)) :subgoals ((address-in-front ?self ?ad ?st) (at-address ?self ?ad ?st))) ((at-address ?self ?ad ?st) :percepts ((self ?self) (street ?st)) :start ((not (not-hitting-pedestrians ?self)) (address-behind ?self ?ad ?st)) :subgoals ((not-hitting-pedestrians ?self) (at-address ?self ?ad ?st))) ((at-address ?self ?ad ?st) :percepts ((self ?self) (street ?st)) :start ((not (at-desired-speed ?self)) (address-behind ?self ?ad ?st)) :require ((not-hitting-pedestrians ?self)) :subgoals ((at-desired-speed ?self) (at-address ?self ?ad ?st))) tended formalism.... ..."

### Table 2: Variational calculation for the nucleon self-energy in the Wick-Cutkosky model using the `extended apos; parametrization (87) for the retardation function. The parameters xi; wi ; i = 1; 2 obtained from minimizing Eq. (92) are given as well as for di erent values of the coupling constant . They are constrained such that the correct elastic threshold is obtained. The dimensionless strength parameters x1 and x2 are de ned in Eqs. (93) and ( 94). The lower part of the table lists the mass M1, the value of the pro le function at E = 0, the rst order residue (see (II)) and the root-mean-square radius (57) of the dressed particle.

"... In PAGE 16: ... Thereforers(1) thresh ? M = pM2 + 2A0E0 ? M (76) which should be equal to the meson mass m. Using Table2 in (II) the right-hand side of Eq. (76) is found to vary between 408 MeV at = 0:1 and 275 MeV at = 0:8 .... In PAGE 19: ...90) was used to eliminate the parameter C2 via Eq. (89) so that a 4-parameter minimization of Eq. (92) had to be performed. Table2 gives the parameters of the `extended apos; parametrization obtained in this way as well as some quantities of interest derived from them. In view of the expressions (80) and (84) for the variational retardation function we write the strength parameters as C1 = x1 g2 32 2 = x1 8 M2 (93) C2 = x2 ms 2 m M 3 (94) and list the dimensionless numbers x1; x2.... In PAGE 20: ... However, there are additional higher thresholds coming from the second branch point E0 0 = w1 in the pro le function of the `extended apos; parametrization. Since w1 is decreasing for larger coupling constants (see Table2 ) these additional thresholds may even come to lie below the rst inelastic threshold ( at jpj = 214:2 MeV ) which is seen, e.... In PAGE 23: ... In addition, the second factor is 1+O(m2=M2), the form factor is practically one and the last factor also turns out to be very close to one (except at = 0:8 where it is 1:17 ). Thus for nearly all accessible coupling constants one has the simple result U0 4 x2 : (104) From Table2 we see that the dimensionless parameter x2 grows from 2:2 at small coupling to over 7 at = 0:7 before declining again and that the approximation (104) accounts rather well for the values el= tot listed in Table 3. The reverse procedure also works satisfactorily as can be seen in Fig.... In PAGE 24: ...The full line gives the result using the `extended apos; parametrization from Table2 , whereas the dotted line follows from a variational calculation in which the strength parameter x2 = 4 has been kept xed. Figure 10: Argand plot for the s-wave scattering amplitude with the `extended apos; parametrization of the retardation function at = 0:5.... ..."

### Table 1. Preliminary Results from Multilevel Models for the Extended PISA Database (new countries denoted by + ).

"... In PAGE 4: ... Preliminary Results and Discussion Preliminary results confirmed that the BFLPE does extend to non-industrial and non- western countries. As seen in Table1 , the effect of individual achievement on academic self- concept was positive for all countries, including the additional countries, with the exception ... In PAGE 5: ...and negative effects in the remaining two countries that were not statistically significant. These results were replicated in the present investigation for the original countries (refer Table1 ). Furthermore, the effect of school-average achievement on academic self-concept was significantly negative in six of the eight additional countries, while the remaining two displayed a positive effect.... In PAGE 5: ... Since the results for this country are in the opposite direction from those found normally, further investigation is necessary to determine the reasons behind this abnormal finding. Table1 also demonstrates that the effect of individual achievement on academic self-concept (excluding Romania) varied from country to country (.... ..."

### Table 3. Proteins rejected by the self-consistent burial optimization

2002

"... In PAGE 6: ... Four proteins were removed from the initial set, leaving a final training set of seventy proteins. It is interesting to note that every rejected protein had one of two features; they were either biologically active as a dimer or a tetramer, or formed an extended structure (see Table3 ). This was a comforting result, as (barring an unlikely event that unstable structures in our initial set outnumbered the stable ones) it was exactly what we expected.... ..."

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### Table 2: Number of Indecomposable Self-Dual Additive Codes Over GF(4) by Distance

2005

"... In PAGE 2: ... We extend this sequence from n = 9 to n = 12 both for indecomposable and de- composable codes as shown in table 1. Table2 shows the number of inequivalent indecomposable codes by distance. The distance, d, of a self-dual additive code over GF(4), C, is the smallest weight (i.... ..."

Cited by 10

### Table 1: Average payoff in self-play by algorithm, as a function of the number of players.

2007

"... In PAGE 19: ... One could extend this approach to add different default behaviors for individual games and then use the methods proposed by McCracken and Bowling [23] to guarantee that the security value is always achieved. In Table1 we show the payoff for different algorithms in self-play, that is, when all players use the same algorithm. With an explicit mechanism for sig-... ..."

Cited by 2

### Table 3: Results on RCPSP with a self-adapting shaving and a time-limit of 1800s

"... In PAGE 5: ...8 1 0 5 10 15 20 25 30 35 40 Search depth Actual shaving ratio Target shaving ratio Given that self-adapting shaving slightly improves the per- formances within the same time limit of 300s, we used this configuration with an extended time-limit of 1800s. The re- sults are summarized on Table3 . Out of the 617 previously open instances, we improve 193 lower-bounds (that is more than 31% of the previously open instances) with an average gap reduction of 61.... ..."