Jay H. Beder
Department of Mathematical Sciences
University of Wisconsin-Milwaukee
The main result (Theorem 3.7) asserts that for an arbitrary (simple) fraction, maximum resolution = 1 + maximum strength. The 2004 paper in Utilitas (below) only asserted ≥. No use is made of wordlengths, but rather just the Box-Hunter definition of resolution.
Xu and Wu (2001) defined the generalized wordlength pattern (GWLP) of a design by indexing the levels of each factor by a cyclic group. When the number of levels of a factor is composite, other choices of abelian group are possible. We show that the GWLP is independent of this choice, although the so-called J-characteristics (defined by Ai and Zhang, 2004) are not.
This is the third in a series, following Beder&Gomulkiewicz (1998) below. We compute the selection differential and (especially) the selection gradient for a Gaussian trait with a "Gaussian" fitness function that models optimizing selection. The paper relies in part on Lukic&Beder (2001).
This is a follow-up to the paper, "On Rao's inequalities for arrays of strength d," below, but with a simpler approach. It includes a couple of applications to aliasing in non-regular fractions.
The article reviews two papers of Fortet and some related results, but Section 3 of the published version is rather out of date. An updated (unpublished) version is available online in dvi , ps (postscript), or pdf format. Section 3 summarizes results from Lukic and Beder (2001) below.
This is a follow-up of Gomulkiewicz and Beder (1996) below, and includes (among other things) the rigorous development for infinite-dimensional traits of the so-called Breeder's Equation. Applications show how to compute gradients.
None of the conjectures of this paper panned out.The conjecture on complex Hadamard matrices was known to be incorrect at the time I wrote the paper, as pointed out to me by Prof. C. H. Cooke. A corrected version of the paper was actually accepted by the editor of that special issue of JSPI before it went to press, but for reasons that I was unable to ascertain the uncorrected version is the one that was published. Hence the Erratum. I was also required to eliminate from the Erratum any reference to editorial error.
When the uncorrected version appeared, Prof. Cooke published a note on the subject ( MR -- 2001a:05026 ).
The remaining conjectures of this paper have been disproved by a more extensive computer search than I was able to do at the time. See Dursun A. Bulutoglu, David M. Kaziska, A counterexample to Beder's conjectures about Hadamard matrices, JSPI, 139(9), 2009, 3381-3383.
This gives a rigorous development of the modeling of infinite-dimentional traits, in particular the selection differential and selection gradient. Lost in the biology is an interesting (to me) "derivative" which (I think) may be useful in other applications: The functional gradient of E_m(W), where m is the mean of a Gaussian process and W is a function of the process. (The analog in multivariate analysis would be the directional derivative of E(W) with respect to the mean vector.)
I mention this mainly because the title scans in perfect dactylic tetrameter. However, the contents were not without value. The only paper that comes directly out of the dissertation is the "Estimating ... unknown scale parameter" (1988). But the material became the foundation for the two main sieve papers (Ann. Statist., 1987 and 1988).