Predictor-corrector methods of Runge-Kutta type for stochastic differential equations

In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge-Kutta (RK) correctors for solving stochastic differential equations. Using the colored rooted tree theory and stochastic B-series, the order condition theorem is derived for constructing stochastic RK methods based on PC implementations. We also present detailed order conditions of the PC methods using stochastic implicit RK correctors with strong global order 1.0 and 1.5. A two-stage implicit RK method with strong global order 1.0 and a four-stage implicit RK method with strong global order 1.5 used as the correctors are constructed in this paper. The mean-square stability properties and numerical results of the PC methods based on these two implicit RK correctors are reported.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

Fluid-mobile trace element constraints on the role of slab melting and implications for Archaean crustal growth models

We use published and new trace element data to identify element ratios which discriminate between arc magmas from the supra-subduction zone mantle wedge and those formed by direct melting of subducted crust (i.e. adakites). The clearest distinction is obtained with those element ratios which are strongly fractionated during refertilisation of the depleted mantle wedge, ultimately reflecting slab dehydration. Hence, adakites have significantly lower Pb/Nd and B/Be but higher Nb/Ta than typical arc magmas and continental crust as a whole. Although Li and Be are also overenriched in continental crust, behaviour of Li/Yb and Be/Nd is more complex and these ratios do not provide unique signatures of slab melting. Archaean tonalite-trondhjemite-granodiorites (TTGs) strongly resemble ordinary mantle wedge-derived arc magmas in terms of fluid-mobile trace element content, implying that they-did not form by slab melting but that they originated from mantle which was hydrated and enriched in elements lost from slabs during prograde dehydration. We suggest that Archaean TTGs formed by extensive fractional crystallisation from a mafic precursor. It is widely claimed that the time between the creation and subduction of oceanic lithosphere was significantly shorter in the Archaean (i.e. 20 Ma) than it is today. This difference was seen as an attractive explanation for the presumed preponderance of adakitic magmas during the first half of Earth's history. However, when we consider the effects of a higher potential mantle temperature on the thickness of oceanic crust, it follows that the mean age of oceanic lithosphere has remained virtually constant. Formation of adakites has therefore always depended on local plate geometry and not on potential mantle temperature.

Fibroblast growth factor receptor 4 (FGFR4) expression in newborn murine calvaria and primary osteoblast cultures

Fibroblast growth factor receptor (FGFR) signalling is important in the initiation and regulation of osteogenesis. Although mutations in FGFR1, 2 and 3 genes are known to cause skeletal deformities, the expression of FGFR4 in bony tissue remains unclear. We have investigated the expression pattern of FGFR4 in the neonatal mouse calvaria and compared it to the expression pattern in cultures of primary osteoblasts. Immunohistochemistry demonstrated that FGFR4 was highly expressed in rudimentary membranous bone and strictly localised to the cellular components (osteoblasts) between the periosteal and endosteal layers. Cells in close proximity to the newly formed osteoid (preosteoblasts) also expressed FGFR4 on both the endosteal and periosteal surfaces. Immunocytochemical analysis of primary osteoblast cultures taken from the same cranial region also revealed high levels of FGFR4 expression, suggesting a similar pattern of cellular expression in vivo and in vitro. RT-PCR and Western blotting for FGFR4 confirmed its presence in primary osteoblast cultures. These results suggest that FGFR4 may be an important regulator of osteogenesis with involvement in preosteoblast proliferation and differentiation as well as osteoblast functioning during intramembranous ossification. The consistent expression of FGFR4 in vivo and in vitro supports the use of primary osteoblast cultures for elucidating the role of FGFR4 during osteogenesis.

Finite, three-dimensional adsorbed phase growth in activated carbon mesopores

The role of PACs (primary adsorption centers) in the mesopore (i.e., transport) region of activated carbons during adsorption of polar species, such as water, is unclear. A classical model of three-dimensional adsorption on finite PACs is presented. The model is a preliminary, theoretical investigation into adsorption on mesopore PACs and is intended to give some insight into the energetic and physical processes at work. Work processes are developed to obtain isotherms and three-dimensional sorbate growth on PACs of varying size and energetic characteristics. The work processes allow two forms of adsorbed phase growth: densification at constant boundary and boundary growth at constant density. Relatively strong sorbate-sorbent interactions and strong surface tension favor adsorbed phase densification over boundary growth. Conversely, relatively weak sorbate-sorbent interactions and weak surface tension favor boundary growth over densification. If sorbate-sorbate interactions are strong compared to sorbate-sorbent interactions, condensation with hysteresis occurs. This can also give rise to delayed boundary growth, where all initial adsorption occurs in the monolayer only. The results indicate that adsorbed phase growth on PACs may be quite complex.

Control of ovulation with a GnRH agonist after superstimulation of follicular growth in buffalo: fertilization and embryo recovery

The potential to use a GnRH agonist bioimplant and injection of exogenous LH to control the time of ovulation in a multiple ovulation and embryo transfer (MOET) protocol was examined in buffalo. Mixed-parity buffalo (Bubalus bubalis; 4-15-year-old; 529 13 kg LW) were randomly assigned to one of five groups (n = 6): Group 1, conventional MOET protocol; Group 2, conventional MOET with 12 It delay in injection of PGF(2alpha); Group 3, implanted with GnRH agonist to block the pre-ovulatory surge release of LH; Group 4, implanted with GnRH agonist and injected with exogenous LH (Lutropin(R), 25 mg) 24 h after 4 days of superstimulation with FSH; Group 5, implanted with GnRH agonist and injected with LH 36 h after superstimulation with FSH. Ovarian follicular growth in all buffaloes was stimulated by treatment with FSH (Folltropin-V(R), 200 mg) administered over 4 days, and was monitored by ovarian ultrasonography. At the time of estrus, the number of follicles greater than or equal to8 mm. was greater (P < 0.05) for buffaloes in Group 2 (12.8) than for buffaloes in Groups 1 (8.5), 3 (7.3), 4 (6.1) and 5 (6.8), which did not differ. All buffaloes were mated by AI after spontaneous (Groups 1-3) or induced (Groups 4 and 5) ovulation. The respective number of buffalo that ovulated, number of corpora lutea, ovulation rate (%), and embryos + oocytes recovered were: Group 1 (2, 1.8 +/- 1.6, 18.0 +/- 13.6, 0.2 +/- 0.2); Group 2 (4, 6.1 +/- 2.9, 40.5 +/- 17.5, 3.7 +/- 2.1); Group 3 (0, 0, 0, 0); Group 4 (6, 4.3 +/- 1.2, 69.3 +/- 14.2, 2.0 +/- 0.9); and Group 5 (1, 2.5 +/- 2.5, 15.5 +/- 15.5, 2.1 +/- 2.1). All buffaloes in Group 4 ovulated after injection of LH and had a relatively high ovulation rate (69%) and embryo recovery (46%). It has been shown that the GnRH agonist-LH protocol can be used to improve the efficiency of MOET in buffalo. (C) 2002 Elsevier Science Inc. All rights reserved.

A probabilistic analysis of Clostridium perfringens growth during food service operations

The purpose of this study was threefold: first, the study was designed to illustrate the use of data and information collected in food safety surveys in a quantitative risk assessment. In this case, the focus was on the food service industry; however, similar data from other parts of the food chain could be similarly incorporated. The second objective was to quantitatively describe and better understand the role that the food service industry plays in the safety of food. The third objective was to illustrate the additional decision-making information that is available when uncertainty and variability are incorporated into the modelling of systems. (C) 2002 Elsevier Science B.V. All rights reserved.

Fetal Growth Spurt and Pregestational Diabetic Pregnancy

OBJECTIVE - To assess the timing of fetal growth spurt among pre-existing diabetic pregnancies (types 1 and 2) and its relationship with diabetic control. To correlate fetal growth acceleration with factors that might influence fetal growth. RESEARCH DESIGN AND METHODS - This retrospective study involved all pregestational diabetic pregnancies delivered at a tertiary obstetric hospital in Australia between 1 January 1994 and 31 December 1999. Pregnancies with major congenital fetal anomalies, multiple pregnancies, small-for-gestational-age pregnancies (90th centile for gestation) were compared with babies with normal birth weights. RESULTS- A total of 101 diabetic pregnancies were included. Diabetic mothers, who had LGA babies, had significantly higher prepregnancy body weight and BMI (P < 0.05). There were no differences in maternal age or parity among the two groups. There were also no differences in the first-, second-, and third-trimester HbA(1c) levels between the two groups. The abdominal circumference z-scores were significantly higher for LGA babies from 18 weeks and thereafter. The differences increased progressively as the gestation advanced. Maximum difference was noted in the third trimester (30-38 weeks). CONCLUSIONS - Fetal growth acceleration in LGA fetuses of diabetic mothers starts in the second trimester, from as early as 18 weeks. In this study, glucose control did not appear to have a direct effect on the incidence of LGA babies, and such observation might result from the effects of other confounding factors.

Keratinocyte Growth factor (KGF) in hematology and oncology

Keratinocyte Growth factor (KGF) is an epithelial cell growth factor of the fibroblast growth factor family and is produced by fibroblasts and microvascular endothelium in response to proinflammatory cytokines and steroid hormones. KGF is a heparin binding growth factor that exerts effects on epithelial cells in a paracrine fashion through interaction with KGF receptors. Preclinical data has demonstrated that KGF can prevent lung and gastrointestinal toxicity following chemotherapy and radiation and preliminary clinical data in the later setting supports these findings. In the experimental allogeneic bone marrow transplant scenario KGF has shown significant ability to prevent graft-versus-host disease by maintaining gastrointestinal tract integrity and acting as a cytokine shield to prevent subsequent proinflammatory cytokine generation. Within this setting KGF has also shown an ability to prevent experimental idiopathic pneumonia syndrome by stimulating production of surfactant protein A, promoting alveolar epithelialization and attenuating immune-mediated injury. Perhaps most unexpectantly, KGF appears able to maintain thymic function during allogeneic stern cell transplantation and so promote T cell engraftment and reconstitution. These data suggest that KGF will find a therapeutic role in the prevention of epithelial toxicity following intensive chemotherapy and radiotherapy protocols and in allogeneic stem cell transplantation.

Placental growth hormone is not suppressed by oral glucose loading in normal human pregnancy

Placental growth hormone (PGH) progressively replaces pituitary growth hormone in the maternal circulation from mid-gestation onwards in human pregnancy. Our previous investigations have shown that placental growth hormone concentrations correlate well with foetal growth. Despite the apparent correlation between PGH and birthweight, the physiology of its secretion during pregnancy has not been well defined. We investigated the response of maternal serum PCH to oral glucose loading in pregnant women (n = 24) who demonstrated normal glucose tolerance at a mean gestation of 29 weeks. Mean (SEM) fasting PGH concentrations were high (36.9 [6.4] ng/ml). No suppression of PGH was noted at one, two or three hours after a 75 g oral glucose load. Similarly, no changes were noted in growth hormone binding protein or in calculated free PGH over the course of the glucose tolerance test. As expected, insulin concentrations rose sixfold and insulin like growth factor binding protein 1 concentrations fell by 20% with glucose loading. Cot-relation analysis showed maternal weight, BMI, fasting serum glucose serum insulin to be significantly correlated with the babies' birthweight. Our results support the proposition that PGH concentrations in maternal serum are not Suppressed by oral glucose loading in non-diabetic mothers.

Suppressor of cytokine signaling 2 regulates neuronal differentiation by inhibiting growth hormone signaling

The intracellular mechanisms that determine the response of neural progenitor cells to growth factors and regulate their differentiation into either neurons or astrocytes remain unclear. We found that expression of SOCS2, an intracellular regulator of cytokine signaling, was restricted to mouse progenitor cells and neurons in response to leukemia inhibitory factor (LIF)-like cytokines. Progenitors lacking SOCS2 produced fewer neurons and more astrocytes in vitro, and Socs2(-/-) mice had fewer neurons and neurogenin-1 (Ngn1)-expressing cells in the developing cortex, whereas overexpression of SOCS2 increased neuronal differentiation. We also report that growth hormone inhibited Ngn1 expression and neuronal production, and this action was blocked by SOCS2 overexpression. These findings indicate that SOCS2 promotes neuronal differentiation by blocking growth hormone-mediated downregulation of Ngn1.