This paper models competing mechanism games as extensive games where the extensive form is incompletely understood by a modeler, typically because the modeler doesn’t see all the messages that are being exchanged and doesn’t understand all the contracts that can be enforced. For this reason, the revelation principle can’t be used to characterize supportable outcomes. The paper provides a relati...

We extend a reciprocity theorem of Stanley about enumeration of integer points in polyhedral cones when one exchanges strict and weak inequalities. The proof highlights the roles played by Cohen–Macaulayness and canonical modules. The extension raises the issue of whether a Cohen–Macaulay complex of dimension d embedded piecewise-linearly in R is necessarily a d-ball. This is observed to be tru...

Crossover and noncrossover recombinants can form by two different pathways during meiotic recombination in Saccharomyces cerevisiae. The MER3 gene is known to affect selectively crossover, but not noncrossover, recombination. The Mer3 protein is a DNA helicase that unwinds duplex DNA in the 3' to 5' direction. To define the underlying molecular steps of meiotic recombination, we investigated th...

Schizosaccharomyces pombe rec mutants were previously isolated on the basis of their deficiency in meiotic recombination at the ade6 locus. We surveyed their meiotic recombination deficiencies at and between other loci. In rec10 mutants recombinant frequencies in the approximately 2-Mb region surrounding the ade6 locus were reduced 10- to 100-fold, but recombinant frequencies at or between nine...

In this paper, we propose a palindromic quadratization approach, transforming a palindromic matrix polynomial of even degree to a palindromic quadratic pencil. Based on the (S + S−1)-transform and Patel’s algorithm, the structurepreserving algorithm can then be applied to solve the corresponding palindromic quadratic eigenvalue problem. Numerical experiments show that the relative residuals for...

x . In the case that k = n− 1, the polynomial Pn,k(x) takes the form Pn,n−1(x) = (x+ 1) n − x. If n is not a prime, Pn,n−1(x) is reducible over Q. If n = p is prime, the polynomial Pn,n−1(x) = Pp,p−1(x) is irreducible as Eisenstein’s criterion applies to the reciprocal polynomial xPp,p−1(1/x). This note concerns the irreducibility of Pn,k(x) in the case where 1 ≤ k ≤ n− 2. Computations for n ≤ ...

In the yeast Saccharomyces cerevisiae, small chromosomes undergo meiotic reciprocal recombination (crossing over) at rates (centimorgans per kilobases) greater than those of large chromosomes, and recombination rates respond directly to changes in the total size of a chromosomal DNA molecule. This phenomenon, termed chromosome size-dependent control of meiotic reciprocal recombination, has been...

We present here a 16-year-old Turner syndrome patient with a complex karyotype that includes a maternally-inherited balanced translocation between chromosomes 4 and 16 and mosaicism of the isochromosome Xq10. Her karyotype was 45,X,t(4;16) (p15.2;p13.1)[9]/46,X,i(X) (q10),t(4;16)(p15.2;p13.1) [91]. The karyotype of her father was normal, whereas that of her mother had the same balanced transloc...

Significant values of a combinatorial count need not fit the recurrence for the count. Consequently, initial values of the count can much outnumber those for the recurrence. So is the case of the count, Gl(n), of distance-l independent sets on the cycle Cn, studied by Comtet for l ≥ 0 and n ≥ 1 [sic]. We prove that values of Gl(n) are nth power sums of the characteristic roots of the correspond...