Efficient simulation of a Tandem Jackson Network

The two-node tandem Jackson network serves as a convenient reference model for the analysis and testing of different methodologies and techniques in rare event simulation. In this paper we consider a new approach to efficiently estimate the probability that the content of the second buffer exceeds some high level L before it becomes empty, starting from a given state. The approach is based on a Markov additive process representation of the buffer processes, leading to an exponential change of measure to be used in an importance sampling procedure. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer. We prove that when the first buffer is finite, this method yields asymptotically efficient simulation for any set of arrival and service rates. In fact, the relative error is bounded independent of the level L; a new result which is not established for any other known method. When the first buffer is infinite, we propose a natural extension of the exponential change of measure for the finite buffer case. In this case, the relative error is shown to be bounded (independent of L) only when the second server is the bottleneck; a result which is known to hold for some other methods derived through large deviations analysis. When the first server is the bottleneck, experimental results using our method seem to suggest that the relative error is bounded linearly in L.

On the Hamilton-Waterloo problem

The Hamilton-Waterloo problem asks for a 2-factorisation of K-v in which r of the 2-factors consist of cycles of lengths a(1), a(2),..., a(1) and the remaining s 2-factors consist of cycles of lengths b(1), b(2),..., b(u) (where necessarily Sigma(i)(=1)(t) a(i) = Sigma(j)(=1)(u) b(j) = v). In thus paper we consider the Hamilton-Waterloo problem in the case a(i) = m, 1 less than or equal to i less than or equal to t and b(j) = n, 1 less than or equal to j less than or equal to u. We obtain some general constructions, and apply these to obtain results for (m, n) is an element of {(4, 6)1(4, 8), (4, 16), (8, 16), (3, 5), (3, 15), (5, 15)}.

The three-way intersection problem for latin squares

The set of integers k for which there exist three latin squares of order n having precisely k cells identical, with their remaining n(2) - k cells different in all three latin squares, denoted by I-3[n], is determined here for all orders n. In particular, it is shown that I-3[n] = {0,...,n(2) - 15} {n(2) - 12,n(2) - 9,n(2)} for n greater than or equal to 8. (C) 2002 Elsevier Science B.V. All rights reserved.

Genetic Covariation between Serum {gamma}-Glutamyltransferase Activity and Cardiovascular Risk Factors

Background: Several studies have shown that variation in serum gamma-glutamyltransferase (GGT) in the population is associated with risk of death or development of cardiovascular disease, type 2 diabetes, stroke, or hypertension. This association is only partly explained by associations between GGT and recognized risk factors. Our aim was to estimate the relative importance of genetic and environmental sources of variation in GGT as well as genetic and environmental sources of covariation between GGT and other liver enzymes and markers of cardiovascular risk in adult twin pairs. Methods: We recruited 1134 men and 2241 women through the Australian Twin Registry. Data were collected through mailed questionnaires, telephone interviews, and by analysis of blood samples. Sources of variation in GGT, alanine aminotransferase (ALT), and aspartate aminotransferase (AST) and of covariation between GGT and cardiovascular risk factors were assessed by maximum-likelihood model-fitting. Results: Serum GGT, ALT, and AST were affected by additive genetic and nonshared environmental factors, with heritabilities estimated at 0.52, 0.48, and 0.32, respectively. One-half of the genetic variance in GGT was shared with ALT, AST, or both. There were highly significant correlations between GGT and body mass index; serum lipids, lipoproteins, glucose, and insulin; and blood pressure. These correlations were more attributable to genes that affect both GGT and known cardiovascular risk factors than to environmental factors. Conclusions: Variation in serum enzymes that reflect liver function showed significant genetic effects, and there was evidence that both genetic and environmental factors that affect these enzymes can also affect cardiovascular risk. (C) 2002 American Association for Clinical Chemistry.

The validity and heritability of self-report osteoarthritis in an Australian older twin sample

In order to investigate the genetic and environmental antecedents of osteoarthritis (CA), self-report measures of joint pain, stiffness and swelling were obtained from a population-based sample of 1242 twin pairs over 50 years of age. In order to provide validation for these self-report measures, a subsample of 118 twin pairs were examined according to the American College of Rheumatology clinical and radiographic criteria for the classification of osteoarthritis. A variety of statistical methods were employed to identify the model derived from self-report variables which would provide optimal prediction of these standardised assessments, and structural equation modelling was used to determine the relative influences of genetic and environmental influences on the development of osteoarthritis. Significant genetic effects were found to contribute to osteoarthritis of the hands, hips and knees in women, with heritability estimates ranging from 30-46% depending on the site. In addition, the additive genetic effects contributing to osteoarthritis in various parts of the body were confirmed to be the same. Statistically significant familial aggregation of osteoarthritis in men was also observed, but it was not possible to determine whether this was due to genetic or shared environmental effects.

Pea rms6 mutants exhibit increased basal branching

Our studies on two branching mutants of pea (Pisum sativum L.) have identified a further Ramosus locus, Rms6, with two recessive or partially recessive mutant alleles: rms6-1 (type line S2-271) and rms6-2 (type line K586). Mutants rms6-1 and rms6-2 were derived from dwarf and tall cultivars, Solara and Torsdag, respectively. The rms6 mutants are characterized by increased branching from basal nodes. In contrast, mutants rms1 through rms5 have increased branching from both basal and aerial (upper stem) nodes. Buds at the cotyledonary node of wild-type (WT) plants remain dormant but in rms6 plants these buds were usually released from dormancy. Their growth was either subsequently inhibited, sometimes even prior to emergence above ground, or they grew into secondary stems. The mutant phenotype was strongest for rms6-1 on the dwarf background. Although rms6-2 had a weak single-mutant phenotype, the rms3-1 rms6-2 double mutant showed clear transgression and an additive branching phenotype, with a total lateral length almost 2-fold greater than rms3-1 and nearly 5-fold greater than rms6-2 . Grafting studies between WT and rms6-1 plants demonstrated the primary action of Rms6 may be confined to the shoot. Young WT and rms6-1 shoots had similar auxin levels, and decapitated plants had a similar magnitude of response to applied auxin. Abscisic acid levels were elevated 2-fold at node 2 of young rms6-1 plants. The Rms6 locus mapped to the R to Gp segment of linkage group V (chromosome 3). The rms6 mutants will be useful for basic research and also have possible agronomical value.

Heritabilities of Apolipoprotein and Lipid Levels in Three Countries

This study investigated the influence of genes and environment on the variation of apolipoprotein and lipid levels, which are important intermediate phenotypes in the pathways toward cardiovascular disease. Heritability estimates are presented, including those for apolipoprotein E and All levels which have rarely been reported before. We studied twin samples from the Netherlands (two cohorts; n = 160 pairs, aged 13-22 and n = 204 pairs, aged 34-62), Australia (n = 1362 pairs, aged 28-92) and Sweden (n = 302 pairs, aged 42-88). The variation of apolipoprotein and lipid levels depended largely on the influences of additive genetic factors in each twin sample. There was no significant evidence for the influence of common environment. No sex differences in heritability estimates for any phenotype in any of the samples were observed. Heritabilities ranged from 0.48-0.87, with most heritabilities exceeding 0.60. The heritability estimates in the Dutch samples were significantly higher than in the Australian sample. The heritabilities for the Swedish were intermediate to the Dutch and the Australian samples and not significantly different from the heritabilities in these other two samples. Although sample specific effects are present, we have shown that genes play a major role in determining the variance of apolipoprotein and lipid levels in four independent twin samples from three different countries.

The metamorphosis of lambda-fold K-3,K-3-designs into lambda-fold 6-cycle systems

In this paper necessary and sufficient conditions are given for the metamorphosis of a lambda-fold K-3,K-3-design of order n into a lambda-fold 6-cycle system of order n, by retaining one 6-cycle subgraph from each copy of K-3,K-3, and then rearranging the set of all the remaining edges, three from each K-3,K-3, into further 6-cycles so that the result is a lambda-fold 6-cycle system.

Trade spectra of complete partite graphs

The trade spectrum of a graph G is essentially the set of all integers t for which there is a graph H whose edges can be partitioned into t copies of G in two entirely different ways. In this paper we determine the trade spectrum of complete partite graphs, in all but a few cases.

Factorizations of and by powers of complete graphs

Let K-k(d) denote the Cartesian product of d copies of the complete graph K-k. We prove necessary and sufficient conditions for the existence of a K-k(r)-factorization of K-pn(s), where p is prime and k > 1, n, r and s are positive integers. (C) 2002 Elsevier Science B.V. All rights reserved.