Form invariance and implicit parallelism

Holland's schema theorem (an inequality) may be viewed as an attempt to understand genetic search in terms of a coarse graining of the state space. Stephens and Waelbroeck developed that perspective, sharpening the schema theorem to an equality. Of particular interest is a "form invariance" of their equations; the form is unchanged by the degree of coarse graining. This paper establishes a similar form invariance for the more general model of Vose et al. and uses the attendant machinery as a springboard for an interpretation and discussion of implicit parallelism.

The simple genetic algorithm and the Walsh transform: Part I, Theory

This paper is the first part of a two-part series. It proves a number of direct relationships between the Fourier transform and the simple genetic algorithm. (For a binary representation, the Walsh transform is the Fourier transform). The results are of a theoretical nature and are based on the analysis of mutation and crossover. The Fourier transform of the mixing matrix is shown to be sparse. An explicit formula is given for the spectrum of the differential of the mixing transformation. By using the Fourier representation and the fast Fourier transform, one generation of the infinite population simple genetic algorithm can be computed in time O(cllog2(3)), where c is arity of the alphabet and l is the string length. This is in contrast to the time of O(c3l) for the algorithm as represented in the standard basis. There are two orthogonal decompositions of population space that are invariant under mixing. The sequel to this paper will apply the basic theoretical results obtained here to inverse problems and asymptotic behavior.

The simple genetic algorithm and the Walsh transform: Part II, The inverse

This paper continues the development, begun in Part I, of the relationship between the simple genetic algorithm and the Walsh transform. The mixing scheme (comprised of crossover and mutation) is essentially "triangularized" when expressed in terms of the Walsh basis. This leads to a formulation of the inverse of the expected next generation operator. The fixed points of the mixing scheme are also determined, and a formula is obtained giving the fixed point corresponding to any starting population. Geiringer's theorem follows from these results in the special case corresponding to zero mutation.

Molecular characterization of leukocyte adhesion deficiency in six patients

Leukocyte adhesion deficiency (LAD) is caused by defects in the CD18 gene, which codes for the common beta 2 subunit of the leukocyte integrins LFA-1, Mac-1 and p150,95. Failure to produce a functional beta 2 subunit results in the defective expression of all three leukocyte integrins, and the leukocytes of LAD patients have subnormal adhesion properties. Six patients with LAD were studied. Patient B was homozygous and carried a G284S mutation. A two-bp (GA) deletion at position 1256 (1256 delta GA) was found in the cDNA of patient C, who also had an abnormally large mRNA of 4.3 kb. Patients E and K were siblings and were heterozygous at the genomic level. One defective allele contained a mutation in intron 6/7 which created a preemptive 3' splice site. The resulting mRNA has 12 extra bases at the junction of exons 6 and 7, coding for four extra residues PSSQ in the protein. The same allele also carried a R586W mutation. The other allele was transcribed at a low level and was not characterized. Patient G carried a L149P mutation in one allele; again, the other allele was not characterized due to low transcription levels. Patient R carried two mutant alleles with G284S and R593C mutations respectively. The G284S mutation and the 1256 delta GA deletion have not been reported previously. CD18 cDNA carrying the abnormalities were cotransfected with normal CD11a or CD11b cDNA into COS cells. Expression of the LFA-1 (CD11a/CD18) and Mac-1 (CD11b/CD18) antigens on COS cells was not detected, suggesting that these two mutations are sufficient to account for LAD.

The gene organisation of the human beta 2 integrin subunit (CD18)

We have studied the gene of the human beta 2 integrin subunit (CD18) and found it to be organised into 16 exons spanning a region of about 40 kb. All exon/intron boundaries conform to the GT/AG splicing consensus. The exons coding for the cysteine-rich region, which has been postulated to consist of 3 or 4 repeating elements, are not organised correspondingly. Transcription of the gene initiates from multiple sites which may be due to the absence of an upstream TATA box. The polyadenylation site is also heterogeneous. Five different sites were identified over a stretch of 10 bases.

A study of high copper amalgams. II. Amalgamation on a Hg-plated high copper alloy containing 30 wt% Cu

The amalgamation reaction of a low silver, high copper alloy powder has been investigated by plating tablets of compacted powder with Hg. Both gamma1 Ag-Hg and micro Cu-Sn crystals form on the tablets. In spite of large differences in composition, these tablets amalgamated similarly to the T tablets studied and reported in Part I.

A study of high copper amalgams. I. A comparison of amalgamation on high copper alloy tablets

Two types of high copper alloy powder have been amalgamated by plating tablets of compacted powder with Hg. Gamma1 Ag-Hg crystals form on both types of tablet. On one type, zeta Cu-Sn crystals are also formed. An amalgamation mechanism for this latter type of high copper amalgam is discussed.

The Medical Schools of Toronto

Images