### Table 1. A summary of the results in this paper. The parameter quot; gt; 1 is any arbitrary constant. For the d-dimensional case, M = d i=1ni(ui ? `i + 1), N = max1 i d ni and u` = maxi ui `i . For our biology applications p 100 lt; ` 2 n, t apos; n u+`, m is much

"... In PAGE 6: ... 2.3 Synopsis of Results All our results are summarized in Table1 , except the result that GTile problem is NP-hard in two or more dimensions. Most of our algorithms use simple data structures (such as a double-ended queue) and are easy to implement.... ..."

### Table 1. Log of Observations

"... In PAGE 4: ... Similar resolution and sampling was obtained for the three southerly galaxies by observing in the BnA, CnB and DnC con gurations. Observing dates, eld centers and other particulars are summarized in Table1 . Namely, the galaxy name in column (1), the B1950 pointing center in (2), the observation dates for the three observed con gurations in (3), the central velocity and number of frequency channels in (6) and (7).... ..."

### Table 1 lists the results of several different models for the log of the expected number of faults between 1 April 1994 and 1 April 1996. The predictor variables include log lines=1000 , the log of the number of thousands of lines of code in the module on 1 April 1994, comments included: log deltas=1000 , the (log of the) number of thousands of deltas to the module before 1 April 1994; and age, which measures the average age of the code in the module. Suppose that the deltas to the module occurred at dates d1; ...;dn, measured in years before 1990, and that the numbers of lines added to the module by these deltas are a1; ...;an respectively; then

2000

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### Table 2: Correlation coefficient R between the energy and different native distances.

2003

"... In PAGE 17: ... distance measures. The correlation coefficient R between energy and all the five dif- ferent distance measures can be found in Table2 . From this table we see that the en- ergy correlation is strongest for Dn cont and Dn pow, strong also for Dn HS, and significantly weaker for Dn cRMSD and Dn dRMSD.... In PAGE 17: ... From this table we see that the en- ergy correlation is strongest for Dn cont and Dn pow, strong also for Dn HS, and significantly weaker for Dn cRMSD and Dn dRMSD. From Table2 we also see that log(Dn cRMSD+1) and log(Dn dRMSD+1) are more strongly correlated with energy than Dn cRMSD and Dn dRMSD, respectively. This is not surprising since we have seen that Dn cRMSD is approximately exponentially related to Dn cont, and that Dn cont is very strongly correlated with energy.... ..."

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### Table 2: Dn.

1997

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### Table 1. Nonnesting partitions on Dn by type

1998

"... In PAGE 14: ... For example, there are 3 noncrossing D3-partitions of type (3) but 4 nonnesting partitions of the same kind, namely the 3 nonnesting partitions on B3 of type (3) and the one with blocks f1; ?2; ?3g and f2; 3; ?1g. Table1 shows the number of nonnesting partitions on Dn of type for the partitions of n 6 with at least one part greater than 2. Acknowledgement.... ..."

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### Table 1. Nonnesting partitions on Dn by type

1998

"... In PAGE 14: ... For example, there are 3 noncrossing D3-partitions of type (3) but 4 nonnesting partitions of the same kind, namely the 3 nonnesting partitions on B3 of type (3) and the one with blocks f1; ?2; ?3g and f2; 3; ?1g. Table1 shows the number of nonnesting partitions on Dn of type for the partitions of n 6 with at least one part greater than 2. Acknowledgement.... ..."

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### Table 2: Comparison of Upper Bounds on DN

1997

"... In PAGE 55: ...4 3 10 9 21 6 20 40 17 39 64 11 36 63 87 30 60 86 101 19 54 83 100 109 43 77 97 108 114 24 66 91 105 113 116 47 80 99 110 115 23 61 88 104 112 37 69 93 106 14 45 74 95 22 50 76 8 27 52 13 29 5 15 7 2 Figure 21: Example (N = 10) of the VG-Algorithm Finally, in Table2 , we give a summary of the various upper bounds which have been discussed, in comparison with the actual values of DN. We know (from Corollaries 5.... In PAGE 55: ... However, as DN seems to be diverging from the cubic bounds (and based on other analytical and empirical evidence), we conjecture that DN is, in fact, bounded above by a quadratic in N. Of course, for this to be true, it is su cient (but not necessary) for the trace of the N-triangle generated by the VG-algorithm using the permutation given by equation (136) (the sixth column in Table2 ) to be bounded above by a quadratic in N. If it is true, this latter assertion may be easier to prove.... In PAGE 55: ... Without loss of generality, we state the quadratic bound conjecture as Conjecture 10 There exists some 2 IR such that DN CN for all N 2 IN. For the purpose of comparison, we tabulate this pseudo-bound for = 1:5 in the last column of Table2 ; we do not claim that this value of works for all N 2 IN. 12 Conclusion and Open Problems To conclude, we rst summarize the key results concerning the relationship between max- imizing irregularity (Problem 1) and the Golomb Ruler Problem (Problem 2).... ..."

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