Decompositions of complete graphs into triangles and Hamilton cycles

For all odd integers n greater than or equal to 1, let G(n) denote the complete graph of order n, and for all even integers n greater than or equal to 2 let G,, denote the complete graph of order n with the edges of a 1-factor removed. It is shown that for all non-negative integers h and t and all positive integers n, G, can be decomposed into h Hamilton cycles and t triangles if and only if nh + 3t is the number of edges in G(n). (C) 2004 Wiley Periodicals, Inc.

Storm cycles in the last millennium recorded in Yongshu Reef, southern South China Sea

Large storm-relocated Porites coral blocks are widespread on the reef flats of Nansha area, southern South China Sea. Detailed investigations of coral reef ecology, geomorphology and sedimentation on Yongshu Reef indicate that such storm-relocated blocks originated from large Porites lutea corals growing on the spurs within the reef-front living coral zone. Because the coral reef has experienced sustained subsidence and reef development during the Holocene, dead corals were continuously covered by newly growing coral colonies. For this reason, the coral blocks must have been relocated by storms from the living sites and therefore the ages of these storm-relocated corals should approximate the times when the storms occurred. Rapid emplacement of these blocks is also evidenced by the lack of coral overgrowth, encrustation or subtidal alteration. U-series dating of the storm-relocated blocks as well as of in situ reef flat corals suggests that, during the last 1000 years, at least six strong storms occurred in 1064 +/- 30, 1210 +/- 5-1201 +/- 4, 1336 +/- 9, 1443 +/- 9, 1685 +/- 8-1680 +/- 6, 1872 +/- 15 AD, respectively, with an average 160-year cycle (110-240 years). The last storm, which occurred in 1872 15 AD, also led to mortality of the reef flat corals dated at similar to 130 years ago. Thus, the storm had significant impacts on coral reef ecology and morphology. (C) 2004 Elsevier B.V. All rights reserved.

Packing lambda-fold complete multipartite graphs with 4-cycles

A maximum packing of any lambda-fold complete multipartite graph (where there are lambda edges between any two vertices in different parts) with edge-disjoint 4- cycles is obtained and the size of each minimum leave is given. Moreover, when lambda =2, maximum 4-cycle packings are found for all possible leaves.

Digenean trematodes infecting the tropical abalone Haliotis asinina have species-specific cercarial emergence patterns that follow daily or semilunar spawning cycles

Approximately 1-2% of the tropical abalone Haliotis asinina inhabiting Heron Island Reef are infected with opecoelid digeneans. These largely inhabit the haemocoel surrounding the cerebral ganglia and digestive gland-gonad complex, and infected abalone typically have significantly reduced or ablated gonads. Observations of infected abalone reveal two distinct cercarial emergence patterns, one which correlates tightly with the abalone's highly regular and synchronous fortnightly spawning cycle, and the other which occurs in a circadian pattern. The former appears to be a novel emergence strategy not previously observed in digeneans. While the cercariae in all abalone are morphologically indistinguishable, comparison of sequences from the internal transcribed spacer 2 (ITS 2) region of the ribosomal DNA reveals a 5.7% difference between cercariae displaying different emergence patterns, indicating these are two distinct species that probably belong to the same genus. The ITS 2 sequences of the species with the daily emergence pattern are identical to that of an undescribed adult opecoelid from the gut of the barramundi cod, Cromileptes altivelis. Combined molecular, morphological and emergence data suggest that while these opecoelid cercariae use the same first intermediate host and are closely related species-members of the genus Allopodocotyle-they fill different ecological niches that are likely to include different definitive hosts.

Stability and cycles in a cobweb model with heterogeneous expectations

We investigate the dynamics of a cobweb model with heterogeneous beliefs, generalizing the example of Brock and Hommes (1997). We examine situations where the agents form expectations by using either rational expectations, or a type of adaptive expectations with limited memory defined from the last two prices. We specify conditions that generate cycles. These conditions depend on a set of factors that includes the intensity of switching between beliefs and the adaption parameter. We show that both Flip bifurcation and Neimark-Sacker bifurcation can occur as primary bifurcation when the steady state is unstable.

Complex life cycles and offspring provisioning in marine invertebrates

Offspring size can have pervasive effects throughout an organism's life history. Mothers can make either a few large or many small offspring, and the balance between these extremes is determined by the relationship between offspring size and performance. This relationship in turn is thought to be determined by the offspring's environment. Recently, it has become clear that events in one life-history stage can strongly affect performance in another. Given these strong carryover effects, we asked whether events in the larval phase can change the relationship between offspring size and performance in the adult phase. We manipulated the length of the larval period in the bryozoan Bugula neritina and then examined the relationship between offspring size and various parameters of adult performance under field conditions. We found that despite the adult stage being outplanted into identical conditions, different offspring sizes were predicted to be optimal, depending on the experience of those adults as larvae. This work highlights the fact that the strong phenotypic links between life-history stages may result in optimal offspring size being highly unpredictable for organisms with complex life cycles.

Entangled-state cycles from conditional quantum evolution

A system of cascaded qubits interacting via the one-way exchange of photons is studied. While for general operating conditions the system evolves to a superposition of Bell states (a dark state) in the long-time limit, under a particular resonance condition no steady state is reached within a finite time. We analyze the conditional quantum evolution (quantum trajectories) to characterize the asymptotic behavior under this resonance condition. A distinct bimodality is observed: for perfect qubit coupling, the system either evolves to a maximally entangled Bell state without emitting photons (the dark state) or executes a sustained entangled-state cycle-random switching between a pair of Bell states while emitting a continuous photon stream; for imperfect coupling, two entangled-state cycles coexist, between which a random selection is made from one quantum trajectory to another.

Structure repair of a compacted vertisol with wet-dry cycles and crops

We hypothesized that the four rotation crops: wheat (Triticum aestivum L.), sorghum [Sorghum bicolor (L.) Merr.], lablab [Lablab purpureus (L.) Sweet] and mung bean [ Vigna radiata (L.) R. Wilczek] differ in their ability to repair soil structure. The study was conducted on a Typic Haplustert, Queensland, Australia, locally termed a Black Earth and considered a prime cropping soil. Large (0.5-m depth by 0.3-m diam.) soil cores, collected from compacted wheel furrows in an irrigated cotton (Gossypium hirsutum L.) field, were subjected to three, six, or nine wet-dry cycles that simulated local flood irrigation practices. After each cycle, soil profiles were sampled for clod bulk density, image analysis of soil structure, and evapotranspiration. Generally, all crops improved soil structure over the initial field condition but lablab and mung bean gave improvements to greater depths and more rapidly than wheat and sorghum. Mung bean and lablab caused up to a threefold increase in clod porosity in the 0.1- to 0.4-m soil layer after only three wet-dry cycles, whereas sorghum required nine wet-dry cycles to increase clod porosity in only the 0.2- to 0.3-m layer, and wheat gave no improvement even after nine wet-dry cycles. Image analysis of soil structure showed that lablab and mung bean rapidly (by three wet-dry cycles) produced smaller peds with more interconnected pore space than wheat and sorghum. By nine wet-dry cycles, sorghum achieved deep cracking of the soil but the material between the cracks remained large and dense. Evapotranspiration was double under lablab and mung bean compared with wheat and sorghum. Our results indicate greater cycles of wetting and drying under lablab and mung bean than wheat and sorghum that have led to rapid repair of soil compaction.