Proportionally balanced designs: Some further results and general constructions

Proportionally balanced designs were introduced by Gray and Matters in response to a need for the allocation of markers of the Queensland Core Skills Test to have a certain property. Put simply, markers were allocated to pairs of units in proportions that reflected the relative numbers of markers allocated in total to each unit. In this paper, the first author extends the theoretical results relating to such designs and provides further instances, and two general constructions, in the case that the design comprises blocks of precisely two sizes.

Star factorizations of graph products

A k-star is the graph K-1,K-k. We prove a general theorem about k-star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k-star factorizations of any power (K-q)(S) of a complete graph with prime power order q, products C-r1 x C-r2 x ... x C-rk of k cycles of arbitrary lengths, and any power (C-r)(S) of a cycle of arbitrary length. (C) 2001 John Wiley & Sons, Inc.

Emmetropization in chicks uses optical vergence and relative distance cues to decode defocus

When visual information is confined to one object plane, the emmetropization end-point is adjusted in accord with the corresponding incident optical vergence at the eye [Proceedings of the 7th International Conference on Myopia (2000) 113]. We now report the effect of adding extra visual information beyond the target plane. Visual conditions were controlled using a cone-lens system: black Maltese cross targets on white opaque backgrounds (OMX) were attached to the open faces of 2.5 cm translucent cones fitted with either 0, +25 or +40 D imaging lenses. An alternative target (TMX) was made by substituting the opaque target background for a transparent background, which allowed access to visual information beyond the target plane. The imaging devices were applied to 7-day-old chicks and worn for 4 days. Prior to this treatment, on day 2, some chicks underwent ciliary nerve section (CNS) to preclude accommodation. All treatments were monocular. Refractive errors and axial ocular dimensions were measured using retinoscopy and A-scan ultrasonography under halothane anesthesia. Treatment effects were specified as mean ( +/-S.D.) interocular differences. Eyes with the OMX/ + 40 D lens combination remained emmetropic ( +0.73 +/-3.57 D), consistent with the target plane being approximately conjugate with the retina. Switching to the TMX caused a hyperopic shift in refractive error ( + 3.78 +/- 3.41 D). This relative shift towards hyperopia in switching from the OMX to the TMX target also occurred for the other two lens powers. Thus, the OMX/ + 25 D lens induced myopia ( - 7.00 +/-5.88 D), corresponding to the imposed hyperopic defocus (target plane now imaged behind the retina), and switching to the TMX resulted in a reduction in myopia (-1.73 +/-5.36 D), The OMX/0 D lens combination produced the largest myopic shift, and here, switching to the TMX condition almost eliminated the myopic response (-15.50 +/-6.62 D cf. -0.56 +/-1.24 D). This relative hyperopic shift associated with switching from the OMX to the TMX target was eliminated by CNS surgery. Thus, the two CNS/TMX groups were both more myopic than the equivalent no CNS/TMX groups ( + 40 D lens: -2.66 +/-2.34 D; +25 D lens: -7.97 +/-6.87 D). When the visual information is restricted to one plane, incident optical vergence appears to direct emmetropization. Adding Visual information at other distances produces a shift in the end-point of ernmetropization in the direction of the added information. That these effects are dependent on the integrity of the accommodation system implies that accommodation plays a role in emmetropization and represents the first reported evidence of this kind. Published by Elsevier Science Ltd.

Long-distance signaling and the control of branching in the rms1 mutant of peal

The ramosus (rms) mutation (rms1) of pea (Pisum sativum) causes increased branching through modification of graft-transmissible signal(s) produced in rootstock and shoot. Additional grafting techniques have led us to propose that the novel signal regulated by Rms1 moves acropetally in shoots and acts as a branching inhibitor. Epicotyl interstock grafts showed that wild-type (WT) epicotyls grafted between rms1 scions and rootstocks can revert mutant scions to a WT non-branching phenotype. Mutant scions grafted together with mutant and WT rootstocks did not branch despite a contiguous mutant root-shoot system. The primary action of Rms1 is, therefore, unlikely to be to block transport of a branching stimulus from root to shoot. Rather, Rms1 may influence a long-distance signal that functions, directly or indirectly, as a branching inhibitor. It can be deduced that this signal moves acropetally in shoots because WT rootstocks inhibit branching in rms1 shoots, and although WT scions do not branch when grafted to mutant rootstocks, they do not inhibit branching in rms1 cotyledonary shoots growing from the same rootstocks. The acropetal direction of transport of the Rms1 signal supports previous evidence that the rms1 lesion is not in an auxin biosynthesis or transport pathway. The different branching phenotypes of WT and rms1 shoots growing from the same rms1 rootstock provides further evidence that the shoot has a major role in the regulation of branching and, moreover, that root-exported cytokinin is not the only graft-transmissible signal regulating branching in intact pea plants.

Can long-distance dispersal be inferred from the New Zealand plant fossil record?

New Zealand is generally thought to have been physically isolated from the rest of the world for over 60 million years. But physical isolation may not mean biotic isolation, at least on the time scale of millions of years. Are New Zealand's present complement of plants the direct descendants of what originally rafted from Gondwana? Or has there been total extinction of this initial flora with replacement through long-distance dispersal (a complete biotic turnover)? These are two possible extremes which have come under recent discussion. Can the fossil record be used to decide the relative importance of the two endpoints, or is it simply too incomplete and too dependent on factors of chance? This paper suggests two approaches to the problem-the use of statistics to apply levels of confidence to first appearances in the fossil record and the analysis of trends based on the entire palynorecord. Statistics can suggest that the first appearance of a taxon was after New Zealand broke away from Gondwana-as long as the first appearance in the record was not due to an increase in biomass from an initially rare state. Two observations can be drawn from the overall palynorecord that are independent of changes in biomass: (1) The first appearance of palynotaxa common to both Australia and New Zealand is decidedly non-random. Most taxa occur first in Australia. This suggests a bias in air or water transport from west to east. (2) The percentage of endemic palynospecies in New Zealand shows no simple correlation with the time New Zealand drifted into isolation. The conifer macrorecord also hints at complete turnover since the Cretaceous.

Monocular and binocular distance cues: insights from visual form agnosia I (of III)

The human nervous system constructs a Euclidean representation of near (personal) space by combining multiple sources of information (cues). We investigated the cues used for the representation of personal space in a patient with visual form agnosia (DF). Our results indicated that DF relies predominantly on binocular vergence information when determining the distance of a target despite the presence of other (retinal) cues. Notably, DF was able to construct an Euclidean representation of personal space from vergence alone. This finding supports previous assertions that vergence provides the nervous system with veridical information for the construction of personal space. The results from the current study, together with those of others, suggest that: (i) the ventral stream is responsible for extracting depth and distance information from monocular retinal cues (i.e. from shading, texture, perspective) and (ii) the dorsal stream has access to binocular information (from horizontal image disparities and vergence). These results also indicate that DF was not able to use size information to gauge target distance, suggesting that intact temporal cortex is necessary for learned size to influence distance processing. Our findings further suggest that in neurologically intact humans, object information extracted in the ventral pathway is combined with the products of dorsal stream processing for guiding prehension. Finally, we studied the size-distance paradox in visual form agnosia in order to explore the cognitive use of size information. The results of this experiment were consistent with a previous suggestion that the paradox is a cognitive phenomenon.

Two-dimensional balanced sampling plans excluding contiguous units

A balanced sampling plan excluding contiguous units (or BSEC for short) was first introduced by Hedayat, Rao and Stufken in 1988. These designs can be used for survey sampling when the units are arranged in one-dimensional ordering and the contiguous units in this ordering provide similar information. In this paper, we generalize the concept of a BSEC to the two-dimensional situation and give constructions of two-dimensional BSECs with block size 3. The existence problem is completely solved in the case where lambda = 1.

R-matrices and the tensor product graph method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

A monolithic smoothing-gap algorithm for contact-impact based on the signed distance function

A new algorithm has been developed for smoothing the surfaces in finite element formulations of contact-impact. A key feature of this method is that the smoothing is done implicitly by constructing smooth signed distance functions for the bodies. These functions are then employed for the computation of the gap and other variables needed for implementation of contact-impact. The smoothed signed distance functions are constructed by a moving least-squares approximation with a polynomial basis. Results show that when nodes are placed on a surface, the surface can be reproduced with an error of about one per cent or less with either a quadratic or a linear basis. With a quadratic basis, the method exactly reproduces a circle or a sphere even for coarse meshes. Results are presented for contact problems involving the contact of circular bodies. Copyright (C) 2002 John Wiley Sons, Ltd.