### Table 2 (a) shows the depth of the resulting multicast tree as function of the group size. As expected, the depth of the tree is roughly logarithmic in the group size. In particular, the depth of the tree for a76a43a87 clients is a87 a32a27 a30 which is only a30 a43a58

2002

"... In PAGE 13: ...066 (0.03) (b) Table2 : Results from experiments on Millennium showing the depth of the tree and the number of a25 a17 a43 a13 a11 a22a28a0 a45 a8 a27 a33 a8 a43 messages pro- cessed (standard deviations in parentheses). 6.... ..."

### Table 6 Cross-sectional Regression Analysis Cross-sectional regressions are estimated using the difference between specialist activity variables and market quality variables of non-U.S. and matching U.S. stocks as dependent variables. The independent variables are the differences in the matching variables. Specifically, the dependent variables are the differences in the natural logarithm of absolute closing inventory, participation rates, stabilization rates, percent quoted spreads, percent effective spreads, volatility of trade- to-trade midquote returns, natural logarithm of average quoted depth, percent realized spread, percent effective spread, and percent adverse selection component. The independent variables are the differences in the natural logarithm of price, the natural logarithm of global market capitalization, the difference in open-to- close return volatility, and close-to-open return volatility. P-values are given in italics. Panel A. Developed Market Stocks

"... In PAGE 25: ... The results are presented in Table 6.23 Panel A of Table6 shows that for developed market stocks, most of the inferences drawn from the earlier analysis hold even after controlling for differences across the two samples. However, two notable exceptions exist.... In PAGE 25: ... This suggests that the difference in realized spreads stems from differences in the samples as opposed to real differences in the non-information component of liquidity provision costs. Panel B of Table6 contains the results for the emerging market stocks. With respect to specialist trading, the regression analysis confirms our earlier findings.... In PAGE 25: ...epth is greater for non-U.S. stocks (Lee, Mucklow, and Ready, 1993). Panel B of Table6 also confirms our earlier findings with respect to adverse selection. However, as with developed market stocks, we find no significant difference in realized spreads.... ..."

### Table 2: Results from experiments on Millennium showing the depth of the tree and the number of query distance

2005

"... In PAGE 26: ... To test our implementation for trees with multiple levels, we use D = 4 instead of D = 8 (as used in simulations). Table2 (a) shows the depth of the resulting multicast tree as function of the group size. As expected, the depth of the tree is roughly logarithmic in the group size.... In PAGE 26: ... In particular, the depth of the tree for 64 clients is 4:5 which is only 1:5 times as large as the depth of a perfectly balanced tree with 64 nodes. To evaluate the overhead of the joining procedure, in Table2 (b), we give the number of control messages (i.e.... ..."

Cited by 1

### Table 1. Estimated values of soil thermal di usivity using the six methods. For estimation using the amplitude equation, the maximum and minimum temperature measurements at 1 and 10 cm depths were used whereas for the phase equation, the interval between occurrences of maximum temperatures at 1 and 10 cm were employed. Estimates of using the arctangent and logarithmic method was achieved using temperature measurement at every 6 h at 1 cm and 10 cm depths. The numerical method estimations were based upon the half hourly temperature measurements during the 24 h period at 4 depth levels: 1, 5, 10 and 15 cm. The measured temperatures at 1, 5 and 15 cm were used to estimate the temperature at 10 cm and was compared with the measured 10 cm temperature to obtain the correct choice of . In the harmonic analysis, the 1 cm hourly temperature observations are employed to obtain the amplitude and phase of the rst two harmonics.

### Table 6 and Table 7 show the number of Kbytes required for the ``pinetree apos; apos; and the ``5 trees apos; apos; scenes. Note the direct effect of the resolution of the slice, and the sub-linear dependency in the number of slices. This suggests that it pays off to have more slices. On the other hand, as can be seen in Figure 15, the slice resolution is not that visually critical to the quality of results. One should account the fact that typically such a ray query is only one sample out of many in a ray pencil so that it must not be accurate or in other words, the slice resolution must not be high. Note also that the size of the compressed depth tree is sub-logarithmic in the volume resolution. A 5123 volume of 128Mbytes is compressed down to 1,506Kbytes, about the same size as a 2563 volume of 16Mbytes which is compressed down to 1,118Kbytes.

"... In PAGE 34: ... Almost half of that time is spent on rendering and most of the rest on the construction of the quad-trees. Slice resolution Number of slices 128 256 512 127 130 410 758 255 164 510 906 511 202 610 1,119 Table6 the number of KBytes of memory required for pinetree scene, 7,779 polygons Table 6 and Table 7 show the number of Kbytes required for the ``pinetree apos; apos; and the ``5 trees apos; apos; scenes. Note the direct effect of the resolution of the slice, and the sub-linear dependency in the number of slices.... ..."

### Table 2: Results from experiments on Millennium showing the depth of the tree and the number of D5D9CTD6DD CSCXD7D8CPD2CRCT messages pro- cessed (standard deviations in parentheses).

2002

"... In PAGE 13: ... To test our implementation for trees with multiple levels, we use BW BP BG instead of BW BP BK (as used in simulations). Table2 (a) shows the depth of the resulting multicast tree as function of the group size. As expected, the depth of the tree is roughly logarithmic in the group size.... ..."

### Table 2. A branching strategy based on gap and depth Gap Depth Rule NFW1 NFW2 NFW3 NBEST UPDATE

"... In PAGE 7: ... When a problem is solved using a branching strategy based on gap and depth, the B amp;B code reports a statistical summary of how the different branching rules were used at different levels of the tree. An example of this output, using the branching strategy in Table2 applied to the nug25 problem, is shown in Table 3. Each row reports the fraction of nodes on a given level where each branching rule was applied.... In PAGE 10: ...ig. 1. Performance of estimator on nug25 Est 0) applied to the nug25 problem, using m = 10,000 dives. Both the estimate and the actual values are obtained using the parameters in Table2 . The estimator obtains no values for nodes at levels k 9, but the nodes at these levels are a nontrivial fraction of the total (note the logarithmic scale for the number of nodes).... In PAGE 21: ... The pool factor is the equivalent number of such machines that would have been required to complete the job in the given wall time. In each case the B amp;B algorithm was applied the branching strategy from Table2 , with settings of the gap and depth parameters chosen for the par-... ..."

### Table 2. A branching strategy based on gap and depth Rule Gap Depth NFW1 NFW2 NFW3 NBEST UPDATE

"... In PAGE 7: ... When a problem is solved using a branching strategy based on gap and depth, the B amp;B code reports a statistical summary of how the different branching rules were used at different levels of the tree. An example of this output, using the branching strategy in Table2 applied to the nug25 problem, is shown in Table 3. Each row reports the fraction of nodes on a given level where each branching rule was applied.... In PAGE 10: ...ig. 1. Performance of estimator on nug25 Est 0) applied to the nug25 problem, using m = 10,000 dives. Both the estimate and the actual values are obtained using the parameters in Table2 . The estimator obtains no values for nodes at levels k 10, but the nodes at these levels are a nontrivial fraction of the total (note the logarithmic scale for the number of nodes).... In PAGE 21: ... The pool factor is the equivalent number of such machines that would have been required to complete the job in the given wall time. In each case the B amp;B algorithm was applied using the branching strategy from Table2 , with settings of the gap and depth parameters chosen for the particular problem. Several runs of the estimator described in Section 3 were... ..."

### Table 2. A branchingstrategy based on gap and depth Rule Gap Depth NFW1 NFW2 NFW3 NBEST UPDATE

"... In PAGE 7: ... When a problem is solved using a branching strategy based on gap and depth, the B amp;B code reports a statistical summary of how the different branching rules were used at different levels of the tree. An example of this output, using the branching strategy in Table2 applied to the nug25 problem, is shown in Table 3. Each row reports the fraction of nodes on a given level where each branching rule was applied.... In PAGE 10: ...ig. 1. Performance of estimator on nug25 Est 0) applied to the nug25 problem, using a13 a45 10,000 dives. Both the estimate and the actual values are obtained using the parameters in Table2 . The estimator obtains no values for nodes at levels a37 a5 10, but the nodes at these levels are a nontrivial fraction of the total (note the logarithmic scale for the number of nodes).... In PAGE 21: ... The pool factor is the equivalent number of such machines that would have been required to complete the job in the given wall time. In each case the B amp;B algorithm was applied using the branching strategy from Table2 , with settings of the gap and depth parameters chosen for the particular problem. Several runs of the estimator described in Section 3 were... ..."

### Table 2: Results from experiments on Millennium showing the depth of the tree and the number of a25 a17 a43 a13 a11 a22a28a0 a45

2002

"... In PAGE 13: ... To test our implementation for trees with multiple levels, we use a20 a74a77a87 instead of a20 a74 a17 (as used in simulations). Table2 (a) shows the depth of the resulting multicast tree as function of the group size. As expected, the depth of the tree is roughly logarithmic in the group size.... ..."