String algorithm

Source-filter Synthesis (Subtractive synthesis, Karplus-Strong Plucked string algorithm [Karplus and Strong, 1983])... 

In order to efficiently compute a mountain pass, the "elastic string algorithm" of More and Munson is employed. Briefly stated, the elastic string algorithm takes the possible paths between two points, x and Xb and approximates each one with a piecewise linear path with m breakpoints. Equation 1 now takes the form... 

An interesting property of the elastic string algorithm is that even by choosing the number of breakpoints fairly small, say at m = 20, a very good approximation for the mountain pass is obtained. The maximum length of each segment, fix, are all set to the same value, h, which is chosen to be... 

Recently, the string algorithm was used for finding the transition path in Alanine dipeptide. If one can apply it successfully to a large protein, then this will be the final missing link in the scheme outlined above for studying dynamics in conformation space. 

D. A. Jaffe and J. O. Smith. Extensions of the Karplus-Strong plucked string algorithm. Computer Music Journal 7(2) 56-69 (1983). 

Figure 2-65. This fingerprint was received by hashing, whereas only one part of all the substructures is specified in the illustration. The asterisk indicates the address of a collision in the bit string, generated by the algorithm.

Finally, we mutate each bit of the resulting chromosomes with some small probability - say Pm = 0.05. In our example we find that values of the fifth bit in C4 and sixth bit in C5 are flipped. The resulting strings make up our 2" generation chromosome population. By chance, the first loop through the algorithm has successfully turned up the most-fit chromosome - C4 =(111111)—> /(C4) = 63 = 3969 - but in general the entire procedure would have to be repeated many times to approach the desired solution. 

Algorithmic Complexity Dynamic Measures complexity of given string vice ensemble Hard to compute complexity equated with randomness... 

Suppose a state s is encoded as a binary string of 10 O s and 10 I s , s = 10101010..., While the number of raw bits defining s is huge, its algorithmic complexity is actually very small because it can be reproduced exactly by the following short program . On the other hand, a completely... 

The vector that the genetic algorithm manipulates is known conventionally as a chromosome or a string we shall use the latter terminology in this chapter. The individual units from which each string is constructed, a single x-, y-, or z-coordinate for an atom in this example, are referred to as genes. 

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