Talk:Holland's schema theorem

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Cylinder sets

From what I can tell, a "Holland schema" is the same thing as a cylinder set. Is it different in any way? linas (talk) 21:33, 5 June 2008 (UTC)[reply]

Holland's Schema Theorem is a theorem, not a type of mathimatical set. The article does a poor job of making this clear. It begins with an example involving a mathematical set, which is probably the reason for the confusion. The theorem itself is mentioned near the middle of the page: "... the schema theorem states that short, low-order, schemata with above-average fitness increase exponentially in successive generations." This should be the introduction to the article. -LesPaul75 _talk 20:19, 21 April 2009 (UTC)[reply]

Underpinnings of the theorem

My recollection is poor, but I believe the theorem was broadly extended and "explained" by work by a group of Russians in the 1980's. This work applied the principles of the renormalization group and of universality to show that not only do short, fit schema take over a population, but that, as one approaches a critical point (percolation threshold), longer fit schemata will occur more and more frequently, dominating the population over the shorter schemata. At the critical point, one will get schema at all length scales (critical opalescence). (Fit schemata are called cluster (physics) although that article only mentions clusters of atoms, rather than the phenomenon of clustering in general, for any theory for the RG techniques are applicable). I simply do not remember this work well enough to write about it, and no longer have any copies of any references, but it seems to me to be an important extension of what is otherwise this rather basic theorem. linas (talk) 15:41, 6 June 2008 (UTC)[reply]

Wrong value?

I'm a little bit confused, shouldn't the defining length of 1**0*1 be 6 instead of 5? 77.128.236.210 (talk) 09:02, 14 July 2008 (UTC)[reply]

This is also unclear from the article. It says: "the defining length δ(H) is the distance between the first and last specific positions." But it is not made clear what a "specific position" is. It mentions "fixed positions" and "specific positions" and my best guess is that the "specific positions" are the asterisks in the given string. But if that's the case, then the defining length of 1**0*1 would not be 5 or 6, I suppose it would be 3? -LesPaul75 _talk 20:24, 21 April 2009 (UTC)[reply]

"Who's Holland?"

A natural question the article doesn't stoop to.--Wetman (talk) 16:44, 19 November 2009 (UTC)[reply]

Approximated to Death

Crossover and mutation are sequential operations. If crossover disrupts 50% of schema and mutation disrupts 50% of schema, then the likelihood of a schema surviving crossover and mutation intact is 25% (not 0%). Holland's Schema Theorem is also dealing with uniform mutation. This means that a schema with "n" defining bits has a (1 - Pm)^n chance of surviving mutation (each defining bit has a [1 - Pm] chance of surviving). The crossover term that is used here is fine as long as it is separate from the disruption caused by mutation.