### Table 1 displays the performance extrema for this deterministic proof by contra- diction strategy on the testbed as well as the mean values over all successful runs. The values in brackets indicate the deviation from the mean. Fig. 2 shows the underlying dis- tribution of the run time for these experiments. In fact, the distribution exhibits heavy- tailed behavior [2] which is manifested in the long tail of the distribution stretching for several orders of magnitude.

2001

"... In PAGE 4: ... Table1 . Statistics for successful runs (108 out of 160) on testbed using deterministic strategy.... ..."

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### Table 1 reports the point estimates of the DoF for asset and equity returns in the DJIA basket, as well as for three subsets consisting of the rst, middle, and last 10 names (in alphabetical order). The similarities between the joint tail behavior (as measured by the DoF) of asset and equity returns are quite striking.4

"... In PAGE 11: ... Table1 : Maximum Likelihood Estimates of DoF for DJIA Portfolios 4The range of accepted DoF is very narrow in each case, exhibiting similar behavior to that displayed in Figure 1.... In PAGE 24: ... Intuitively, with only a handful of names in the portfolio, the event that at least two of them default becomes more likely as we increase their tendency to default together. These qualitative relations are consistent with the results reported in Table 6, where we compare the EDL of ve-year rst-, second-, and third-to-default exposure on a ve-name basket using both a Normal copula and a t-copula with 12 DoF (as estimated in Table1 . In both cases, the marginal distributions of default times are assumed to be de ned by a constant yearly hazard rate equal to 1%, recovery rates are known and equal to 40%, and the risk-free discounting curve is at at 2%.... ..."

### Table 1. COTS AV etection rate and Acrobat behavior on embedded malcode. Virus at the head of PDF Virus at the tail of PDF Total virus/worm

### Table 2. For each model, the statistics are averaged over ten independent realizations. The 95% con dence intervals for the last three statistics are given in parenthesis as percentages of their average values. For the mean and standard deviation, the con dence intervals (not shown) are su ciently tight. Both models provide acceptable approximation of the rst-order statistics, with the standard deviation of the F-ARIMA traces being closer to the real one. Also, the M=G=1 traces slightly underestimate the tail behavior, whereas the F-ARIMA traces overestimate it. As shown in the next section, these di erences do not have a noticeable impact on the queueing behavior.

1998

"... In PAGE 16: ... Table2 : Summary statistic of frames sizes in real and synthetic video data. The statistics for each of the two models are based on 10 independent realizations.... ..."

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### Table 2: Relative Error Calculations for Tail Probabilities

"... In PAGE 17: ... Given that Z more faithfully reproduces the ne structure of the in- nitesimal drift and variance of Q, we suspect that one often obtains better approximations to Q by using Z rather than X. In fact, Table2 in Section 7 illustrates that Z estimates steady-state tail probabilities slightly better than X. However, the presence of state dependence in the in nitesimal variance of Z makes it substantially harder to compute transient performance measures for Z than for X.... In PAGE 24: ...safe approach is to explicitly model the reneging. With regard to the quality of our two universal di usion approximations, Table2 suggests that Z outperforms X in some regions of the tail distribu- tion of the steady-state. Given that X and Z di er only in the asymptotic behavior of their corresponding in nitesimal variances, it is perhaps not sur- prising that tail probabilities approximated via Z perform better than those obtained from X (because its in nitesimal variance reproduces more faith- fully that of Q than does X).... ..."

### Table 3. First Stage Cooperation Rates and Test Statistics, Grouped by Punish/Reward Behavior.

1989

"... In PAGE 18: ... behavior is not possible. Table3 summarizes information regarding first-stage cooperation rates, by punish/reward classification. R1 propensities are reported in the upper part of Table 3, while C1 propensities are reported in the lower part of the table.... In PAGE 18: ... Table 3 summarizes information regarding first-stage cooperation rates, by punish/reward classification. R1 propensities are reported in the upper part of Table3 , while C1 propensities are reported in the lower part of the table. In each part, mean cooperation rates for each group appear in the left-most column.... In PAGE 21: ... 18 Despite substantial differences in R and C cooperation rates within sessions, averaging these measures for comparisons across sessions is innocuous. The statistical comparisons reported in Table3 generate essentially identical test statistics when the average of R and C cooperation rates are used as the basis of comparison. Moreover, the correlation between R and C cooperation rates is high.... ..."

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### Table 1: Parameters of the tail asymptote for low-priority waiting times for various values of arrival rates for high and low priority sources The analysis of M=G=1 queues with priorities in [4] suggests that, when 6 = 0; the asymptote may not lead to a good approximation of the exact tail probabilities. This is illustrated in Figures 2, Figures 3. The gures also show another important feature: the asymptote need not be an upper bound for the exact tail probability. However, in general, this need not be true. For instance, in the case of Poisson arrivals for both high and low priority sources, the non-exponential asymptote in Table 14.2 of [4] provides a conservative approximation to the exact tail probability. In the M=G; G=1 model studied in [4], it was observed that, as the low priority arrival increased, the value of exhibited the following behavior: is equal to ?3=2 till a threshold value of the low-priority arrival rate is reached. At this threshold, is equal to ?1=2 and above this threshold, is equal to zero. We numerically study if this behavior holds with MAP arrival processes. We consider an example with the same type of on-off sources as before. We set the high-priority

2000

"... In PAGE 16: ... We use the results in the previous sections to calculate the exact tail probabilities and use the moment-based technique in [1] to compute the asymptote. The parameters of the asymptote, ; and are shown in Table1 for various values of h and l: As can be seen from the table, can be non-negligible, thus leading to non-exponential asymptotics, in general. It is also interesting to note that the so-called e ective bandwidth approximation, e? T , does not change very much as l is changed with h = 0:0625: However, the true asymptote changes signi cantly as revealed by the di erent values for and :... ..."

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### Table 2: Summary of Performance of -estimator on non-heavy-tailed distributions (250 trials each case).

1999

"... In PAGE 13: ... As approaches 2, the estimator shows some downward bias. Table2 shows the performance of the estimator when applied to datasets drawn from a variety of non-heavy-tailed distributions. Again, each row corresponds to the results of 250 trials, and the \% Estimates quot; column counts the percent of times the estimator returned a value.... In PAGE 13: ... Again, each row corresponds to the results of 250 trials, and the \% Estimates quot; column counts the percent of times the estimator returned a value. The rst two sections of Table2 show the estimator apos;s performance on Normal distributions with unit variance and the exponential distribution with CDF P [X x] = 1 ? e? x for = 1. This shows that nite-variance distributions, which tend to Normal when aggregated, can show scaling behavior with close to 2.... In PAGE 13: ... This shows that nite-variance distributions, which tend to Normal when aggregated, can show scaling behavior with close to 2. The next two sections of Table2 shows the estimator apos;s performance on the Lognormal distri- bution: X = e Z where Z N( ; ). For these distributions (the mean of ln X) was 0 and (the standard deviation of ln X) was either 1 or 2.... In PAGE 13: ... Note that when = 2 the estimator cannot distinguish the asymptotically Normal scaling taking place from heavy-tailed scaling. The nal section of Table2 shows the estimator apos;s performance on the Weibull distribution with CDF P [X x] = 1 ? exp(?(x=a))b. In these tests a = 1 and b = e?1.... ..."

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### Table 2: Davis and Resnick (1984) tail index estimate of the US business cycle durations.

"... In PAGE 13: ... Our Davis and Resnick tail index estimates for the US business cycles, along with their 95%-con dence intervals 8 are reported in Table 2. For the three di erentvalues of m, the estimates in Table2 of the tail indices are all between 1 and 3 in magnitude. The smallest and largest point estimate of the tail index both occur when m = 10, with the smallest being =1:246 and the largest =2:5497.... In PAGE 13: ... The smallest and largest point estimate of the tail index both occur when m = 10, with the smallest being =1:246 and the largest =2:5497. Thus, according to the theoretical results of the previous sections, the point estimates of the duration distribution apos;s tail indices found in Table2 give rise to the observation of long memory in real aggregate output. While the point estimates of the tail index are relatively stable for the three di erent values of m, the tail indices estimated con dence intervals are quite sensitive to the choice of m.... In PAGE 13: ... While the point estimates of the tail index are relatively stable for the three di erent values of m, the tail indices estimated con dence intervals are quite sensitive to the choice of m.In Table2 , the con dence intervals for , and are very muchalikeover each tail indices estimate for both small and large values of m. Unfortunately, for m = 8, each indices estimated con dence interval is too large to makeany inference with regards to the presence of occasional long swings in the duration of the US business cycle.... In PAGE 14: ...lack of inference with small m may be due to the small number of NBER de ned business cycles, suggesting that our results with small m may not be reliable. However, when m = 16, all three of the tail indices estimated con dence intervals in Table2 are close to the interval (1;; 3), suggesting that long memory behavior is presentin US macro data. Our estimate of =2:4673 corresponds to a long memory parameter value of d = ;0:2337, which is close to the semi-nonparametric estimate of the long memory parameter, d = ;0:3, calculated by Diebold and Rudebush (1989) for annual real US GNP growth data from 1869 ; 1987.... ..."

### Table 1. Order of behavioral and physiologic testing in HS mice

2006

"... In PAGE 2: ... This means that animals are immunized during the week in which fear conditioning is as- sessed. Table1 gives the order of tests and the age at which they were carried out. Animals.... In PAGE 2: ... At five weeks of age, all HS animals were weighed and implanted with a microchip for identification. A 50-ll blood sample was taken from the tail vein for immunology (this occurs before allergen sensitization), and a 2- mm hole was made in the center of the cartilaginous part of both ears using a metal ear punch (Fisher Scientific, Catalog No 01-337B) (see Table1 for the order of testing). 130... ..."

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