A conjecture on small embeddings of partial Steiner triple systems

A well-known, and unresolved, conjecture states that every partial Steiner triple system of order u can be embedded in a Steiner triple system of order v for all v equivalent to 1 or 3 (mod 6), v greater than or equal to 2u + 1. However, some partial Steiner triple systems of order u can be embedded in Steiner triple systems of order v < 2u + 1. A more general conjecture that considers these small embeddings is presented and verified for some cases. (C) 2002 Wiley Periodicals, Inc.

Tenuous threads, small miracles

With the new Noosa Youth Centre, Deborah Fisher Architects has woven a small yet sophisticated building out of highly constrained and complex circumstances. Douglas Neale explores a project that convinces through its modesty.

Partitioning sets of triples into small planes

We study partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. Our partitions may contain copies of PG(2, 2) only (Fano partitions) or copies of AG(2, 3) only (affine partitions) or copies of some planes of each type (mixed partitions). We find necessary conditions for Fano or affine partitions to exist. Such partitions are already known in several cases: Fano partitions for v = 8 and affine partitions for v = 9 or 10. We construct such partitions for several sporadic orders, namely, Fano partitions for v = 14, 16, 22, 23, 28, and an affine partition for v = 18. Using these as starter partitions, we prove that Fano partitions exist for v = 7(n) + 1, 13(n) + 1, 27(n) + 1, and affine partitions for v = 8(n) + 1, 9(n) + 1, 17(n) + 1. In particular, both Fano and affine partitions exist for v = 3(6n) + 1. Using properties of 3-wise balanced designs, we extend these results to show that affine partitions also exist for v = 3(2n). Similarly, mixed partitions are shown to exist for v = 8(n), 9(n), 11(n) + 1.

Social structure in migrating humpback whales (Megaptera novaeangliae)

Although largely solitary, humpback whales exhibit a number of behaviours where individuals co-operate with one another, for example during bubble net feeding. Such cases could be due to reciprocal altruism brought on by exceptional circumstances, for example the presence of abundant shoaling fish. An alternative explanation is that these behaviours have evolved through kin selection. With little restriction to either communication or movement, diffuse groups of relatives could maintain some form of social organization without the need to travel in tight-nit units. To try to distinguish between these hypotheses, we took advantage of the fact that migrating humpback whales often swim together in small groups. If kin selection is important in humpback whale biology, these groups should be enriched for relatives. Consequently, we analysed biopsy samples from 57 groups of humpback whales migrating off Eastern Australia in 1992. A total of 142 whales were screened for eight microsatellite markers. Mitochondrial DNA sequences (371 bp) were also used to verify and assist kinship identification. Our data add support to the notion that mothers travel with their offspring for the first year of the calf's life. However, beyond the presence of mother-calf/yearling pairs, no obvious relatedness pattern was found among whales sampled either in the same pod or on the same day. Levels of relatedness did not vary between migratory phases (towards or away from the breeding ground), nor between the two sexes considered either overall or in the north or south migrations separately. These findings suggest that, if any social organization does exist, it is formed transiently when needed rather than being a constant feature of the population, and hence is more likely based on reciprocal altruism than kin selection.

QCD thermal phase transition in the presence of a small chemical potential

We propose a new method to investigate the thermal properties of QCD with a small quark chemical potential mu. Derivatives of quark and gluonic observables with respect to mu are computed at mu=0 for two flavors of p4 improved staggered fermions with ma=0.1,0.2 on a 16(3)x4 lattice, and used to calculate the leading order Taylor expansion in mu of the location of the pseudocritical point about mu=0. This expansion should be well behaved for the small values of mu(q)/T(c)similar to0.1 relevant for BNL RHIC phenomenology, and predicts a critical curve T-c(mu) in reasonable agreement with estimates obtained using exact reweighting. In addition, we contrast the case of isoscalar and isovector chemical potentials, quantify the effect of munot equal0 on the equation of state, and comment on the complex phase of the fermion determinant in QCD with munot equal0.

Practical and economic advantages of choice feeding systems for laying poultry

Poultry can be managed under different feeding systems, depending on the husbandry skills and the feed available. These systems include the following: (1) a complete dry feed offered as a mash ad libitum; (2) the same feed offered as pellets or crumbles ad libitum; (3) a complete feed with added whole grain; (4) a complete wet feed given once or twice a day; (5) a complete feed offered on a restricted basis; (6) choice feeding. Of all these, an interesting alternative to offering complete diets is choice feeding which can be applied on both a small or large commercial scale. Under choice feeding or free-choice feeding birds are usually offered a choice between three types of feedstuffs: (a) an energy source (e.g. maize, rice bran, sorghum or wheat); (b) a protein source (e.g. soyabean meal, meat meal, fish meal or coconut meal) plus vitamins and minerals and (c), in the case of laying hens, calcium in granular form (i.e. oyster-shell grit). This system differs from the modern commercial practice of offering a complete diet comprising energy and protein sources, ground and mixed together. Under the complete diet system, birds are mainly only able to exercise their appetite for energy. When the environmental temperature varies, the birds either over- or under-consume protein and calcium. The basic principle behind practising choice feeding with laying hens is that individual hens are able to select from the various feed ingredients on offer and compose their own diet, according to their actual needs and production capacity. A choice-feeding system is of particular importance to small poultry producers in developing countries, such as Indonesia, because it can substantially reduce the cost of feed. The system is flexible and can be constructed in such a way that the various needs of a flock of different breeds, including village chickens, under different climates can be met. The system also offers a more effective way to use home-produced grain, such as maize, and by-products, such as rice bran, in developing countries. Because oyster-shell grit is readily available in developing countries at lower cost than limestone, the use of cheaper oyster-shell grit can further benefit small-holders in these countries. These benefits apart, simpler equipment suffices when designing and building a feed mixer on the farm, and transport costs are lower. If whole (unground) grain is used, the intake of which is accompanied by increased efficiency of feed utilisation, the costs of grinding, mixing and many of the handling procedures associated with mash and pellet preparation are eliminated. The choice feedstuffs can all be offered in the current feed distribution systems, either by mixing the ingredients first or by using a bulk bin divided into three compartments.

Charting the course of ovarian development in vertebrates

The decision of the embryonic gonad to differentiate as either a testis or an ovary is a critical step in vertebrate development. The molecular basis of this decision has been the focus of much study, particularly over the past decade. Here we contrast the knowledge of early gonadal development and the switch to testis differentiation with the lack of molecular understanding of ovarian development at early stages. We review current knowledge regarding mechanisms of ovarian morphogenesis and propose a model for the hierarchical control of development of the fetal ovary, incorporating the few genes already known to be important and several signals or factors that are hypothesised to exist in the early ovary.

An investigation into the possible inhibitory effects of white cypress pine (Callitris glaucophylla) litter on the germination and growth of associated ground cover species

White cypress-pine stands typically support sparse densities of shrubs and grasses. The commonly held opinion is that leaching of allelopathic chemical compounds from cypress-pine litter partly facilitates this exclusion. Germination and growth of cypress pine seedlings do not appear to be similarly affected. This study set out to determine whether cypress litter had a differential effect on germination and growth of cypress-pine seedlings and on associated ground-cover species. Glasshouse trials comparing seedling emergence under cypress- and artificial-litter layers were undertaken. Cypress-pine litter did not have an inhibitory effect on the germination or growth of ground-cover species. In most cases, seedling emergence was facilitated by the application of cypress-pine litter due to its ability to increase the water holding capacity of the underlying soil. Cypress litter did not promote growth of its own seedlings over its competitors except on coarse-textured soils where it provided an ameliorative function to water stress due to the soil's reduced water holding capacity. The inhibition of ground-cover species' germination and growth in pure cypress stands was suggested to be the result of high below-ground resource competition due to the pine's expansive root morphology.