Generalized Markov branching processes

A generalized Markov Brnching Process (GMBP) is a Markov branching model where the infinitesimal branching rates are modified with an interaction index. It is proved that there always exists only one GMBP. An associated differential-integral equation is derived. The extinction probalility and the mean and conditional mean extinction times are obtained. Ergodicity and stability of GMBP with resurrection are also considered. Easy checking criteria are established for ordinary and strong ergodicty. The equilibrium distribution is given in an elegant closed form. The probability meaning of our results is clear and thus explained.

Fitting host-parasitoid models with CV² > 1 using hierarchical generalized linear models

The powerful general Pacala-Hassell host-parasitoid model for a patchy environment, which allows host density–dependent heterogeneity (HDD) to be distinguished from between-patch, host density–independent heterogeneity (HDI), is reformulated within the class of the generalized linear model (GLM) family. This improves accessibility through the provision of general software within well–known statistical systems, and allows a rich variety of models to be formulated. Covariates such as age class, host density and abiotic factors may be included easily. For the case where there is no HDI, the formulation is a simple GLM. When there is HDI in addition to HDD, the formulation is a hierarchical generalized linear model. Two forms of HDI model are considered, both with between-patch variability: one has binomial variation within patches and one has extra-binomial, overdispersed variation within patches. Examples are given demonstrating parameter estimation with standard errors, and hypothesis testing. For one example given, the extra-binomial component of the HDI heterogeneity in parasitism is itself shown to be strongly density dependent.

A class of generalized Lévy Laplacians in infinite dimensional calculus

A class of generalized Lévy Laplacians which contain as a special case the ordinary Lévy Laplacian are considered. Topics such as limit average of the second order functional derivative with respect to a certain equally dense (uniformly bounded) orthonormal base, the relations with Kuo’s Fourier transform and other infinite dimensional Laplacians are studied.

Effect of caffeine ingestion during prolonged exhaustive exercise on salivary immunoglobulin A, alpha-amylase and cortisol

Exercise can have deleterious effects on the secretion of salivary immunoglobulin A (s-IgA), which appears to be related to perturbations in sympatheticoadrenal activation (Teeuw et al., 2004). Caffeine, commonly used for its ergogenic properties is associated with increased sympathetic nervous system activity, and it has been previously shown that caffeine ingestion before intensive cycling enhances s-IgA responses during exercise (Bishop et al., 2006). Therefore, the aim of the present study was to examine the effect of a performance cereal bar, containing caffeine, before and during prolonged exhaustive cycling on exercise performance and the salivary secretion of IgA, alpha-amylase activity and cortisol. Using a randomised cross-over design and following a 10 – 12 hour overnight fast, 12 trained cyclists, mean (SEM) age: 21(1) yr; height: 179(2) cm; body mass: 73.6(2.5) kg; maximal oxygen uptake, VO2max: 57.9(1.2) completed 2.5 h of cycling at 60%VO2max (with regular water ingestion) on a stationary ergometer, which was followed by a ride to exhaustion at 75% VO2max. Immediately before exercise, and after 55 min and 115 min of exercise participants ingested a 0.9 MJ cereal bar containing 45 g carbohydrate, 5 g protein, 3 g fat and 100 mg of caffeine (CAF) or an isocaloric noncaffeine bar (PLA). Unstimulated timed saliva samples were collected immediately before exercise, after 70 min and 130 min of exercise, and immediately after the exhaustive exercise bout. Saliva was analysed for s-IgA, alpha-amylase activity and cortisol concentration. Saliva flow rates were determined to calculate the s-IgA secretion rate. Data were analysed using a 2-way repeated measures ANOVA and post-hoc t-tests with Holm Bonferroni adjustments applied where appropriate. Time to exhaustion was 35% longer in CAF compared with PLA ((2177 (0.2) vs 1615 (0.16) s; P < 0.05)). Saliva flow rate did not change significantly during the exercise protocol. Exercise was associated with elevations in s-IgA concentration (9% increase), s-IgA secretion rate (24% increase) and alpha-amylase activity (224% increase) post-exhaustion (P < 0.01), but there was no effect of CAF on these responses. Salivary cortisol concentration increased by 64% post-exhaustion in the CAF trial only (P < 0.05), indicating an increase in adrenal activity following caffeine ingestion. Values were 35.7 (5.5) and 19.6 (3.4) nmol/L post-exhaustion for CAF and PLA, respectively. These findings show that ingestion of a caffeine containing cereal bar during prolonged exhaustive cycling enhances endurance performance, increases salivary cortisol secretion post-exhaustion, but does not affect the exercise-induced increases in s-IgA or alpha-amylase activity.