### Table 2: True complexes associated to MaWish re ned alignments.

2007

"... In PAGE 11: ... and 3. in both Table2 and 3 have equal hypergeometric score, showing that the coverage, that is, number of proteins of an alignment contained in its best true MIPS module, does not change. Alignment 2.... In PAGE 11: ... Alignment 2. in Table2 covers 50% of the true complex, while its re nement in Table 3 covers the entire true complex (Casein kinase II, consisting of 4 proteins).... ..."

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### Table 4: Mean and Variance of the Approximated ( ^ M) and True (M) Maximum Order Complexity Distribution for Truly Random Sequences

"... In PAGE 12: ...True versus Approximated (m(c; 24) Probability that a random sequence of length n has Maximum Order Complexity of c We can now calculate the approximate expected value and variance of the maximum order complexity. If we let Mn be a random variable that denotes the maximum order complexity of a random sequence of length n, and ^ Mn our approximation to Mn, then we have for an approximate mean E( ^ Mn) = n?1 X c=0 cm(c; n); and an approximate variance Var( ^ Mn) = n?1 X c=0 c2m(c; n) ? n?1 X c=0 c m(c; n)!2 : The results are shown for comparison with the true values in Table4 . We also note that E( ^ Mn) 2 log2 n for large n, the theoretical asymptotic mean of the maximum order complexity.... ..."

### Table 3: Mean and Variance of the Approximated ( ^ Q) and True (Q) Maximum Order Complexity Distribution for Pure Periodically Repeating Sequences

"... In PAGE 9: ...Lemma[2]: The approximate mean and variance of ^ Qk are given by: E( ^ Qk) Pk?1 c=dlog2 ke c q(c; k) = (k ? 1) ? Pk?2 c=dlog2 ke p(c; k); Var( ^ Qk) (k ? 1)2 ? Pk?2 c=dlog2 ke(2c + 1)p(c; k) ? E( ^ Qk)2: The results of these computations are given in Table3 , where they are compared with the true values. The approximation is becoming more accu- rate as k increases.... ..."

### Table 2 Table 2: Complex System OKID Results|The true and identi ed system poles of

"... In PAGE 18: ... Once again, the OKID algorithm at this point generates the model and the Kalman lter. Table2 shows the identi ed version of the complex system versus the true system, and we can see that the frequencies are excellent, and that the damping ratios are very... ..."

### Table 7: Approximated (E( ^ J24)) and True Values (E(J24)) for the Expected Number of Jumps in Maximum Order Complexity in a sequence of length 24

"... In PAGE 14: ... If we let Jn be a random variable given by the number of jumps in the maximum order complexity pro le of a sequence of length n, then E(Jn) = Jn 2n = n?2 X m=0 Sm(2?(m+1) ? 2?n): If J k n is the random variable of the number of jumps of size k in the maximum order complexity pro le of a sequence of length n then E(J k n ) = Jk n 2n = n?k?1 X m=0 Sm 2m+k+1 : We can use our approximation to calculate approximations ^ Jn and ^ J k n to Jn and J k n respectively. Table 6 gives the expected number of jumps of size k in a sequence of length 24 as calculated by our approximation as well as the true value, and Table7 gives the expected number of jumps in a sequence of length n (1 n 24) as calculated by our approximation as well as the true value. 6 Conclusions In this paper we have derived an approximate distribution for the maximum order complexity of random binary sequences, and we have used this approxi- mation to show how to construct statistical tests to identify keystreams that can be simulated by short feedback shift registers.... ..."

### Table 7.2: Recognition of known complexes by surface skin overlap, as a function of the expansion order, N. This table summarises the ability of the docking algorithm to identify the known binding orientations of several protein complexes when compared against 2:5 106 distinct alternative orientations. Each pair of columns gives the rank and docking score of the conformation of the true complex (to within R = 0:5 A) at the given order, N. Excluding the initial integration step, calculation times increase approximately as O(N3), from 35 seconds at N = 10 to 15 minutes at N = 25 on a Silicon Graphics R5000 processor.

### Table 3: Examples not covered by the rst two rules. For the last two examples, the most general complex, ie. apos;true apos;, has the highest LaplaceAccuracy, thus, the third rule is the default rule: (DEFAULT) not sunburned [0 2]. The nal ordered rule list:

### Table 5: Approximated ( ^ Sm) and True Values (Sm) of the total number of sequences of length (m + 2) with a Maximum Order Complexity jump of size One when the (m + 2)nd is added.

### Table 5.1: Complexity of algorithm from different operations perspective, here .n is length of input test vector and C is the number of times while loop is tested true.

2006

### Table 2: Mean absolute deviation between true and recovered signal, for various filters de- scribed in the text. The complexity represents the number of Kalman filter updates (or equiv- alent) required by each filter at each time point, and is linearly related to speed.

1999

"... In PAGE 14: ... Parameter pJ w v h g Value 1=20 p5 100 p0:05 100 Table 1: Parameter values used to generate Figure 6.3 The results are shown in Table2 which gives the mean absolute deviation between the mean of the posterior distribution at time t and the true signal at time t: For this example, the simple SIR filter always diverges before the end of this series, even with sample sizes as large as 20; 000: This is because there always comes a time when the signal... ..."

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