A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

Building better wildlife-habitat models

Wildlife-habitat models are an important tool in wildlife management toda?, and by far the majority of these predict aspects of species distribution (abundance or presence) as a proxy measure of habitat quality. Unfortunately, few are tested on independent data, and of those that are, few show useful predictive st;ill. We demonstrate that six critical assumptions underlie distribution based wildlife-habitat models, all of which must be valid for the model to predict habitat quality. We outline these assumptions in a mete-model, and discuss methods for their validation. Even where all sis assumptions show a high level of validity, there is still a strong likelihood that the model will not predict habitat quality. However, the meta-model does suggest habitat quality can be predicted more accurately if distributional data are ignored, and variables more indicative of habitat quality are modelled instead.

Groups with exponent six

Burnside asked questions about periodic groups in his influential paper of 1902. The study of groups with exponent six is a special case of the study of the Burnside questions on which there has been significant progress. It has contributed a number of worthwhile aspects to the theory of groups and in particular to computation related to groups. Finitely generated groups with exponent six are finite. We investigate the nature of relations required to provide proofs of finiteness for some groups with exponent six. We give upper and lower bounds for the number of sixth powers needed to define the largest 2-generator group with exponent six. We solve related questions about other groups with exponent sis using substantial computations which we explain.

Pharmacokinetics of ciprofloxacin in ICU patients on continuous veno-venous haemodiafiltration

Objectives: To investigate the pharmacokinetics of intravenous ciprofloxacin 200 mg every 8 h in critically ill patients on continuous veno-venous haemodiafiltration (CVVHDF), one form of continuous renal replacement therapy (CRRT). Design and setting: Open, prospective clinical study in a multidisciplinary, intensive care unit in a university-affiliated tertiary referral hospital. Patients: Sis critically ill patients with acute renal failure on CVVHDF. Interventions: Timed blood and ultrafiltrate samples were collected to allow pharmacokinetics and clearances to be calculated of initial and subsequent doses of 200 mg intravenous ciprofloxacin. CVVHD was performed with 1 l/h of dialysate and 2 l/h of predilution filtration solution, producing 3 lih of dialysis effluent. The blood was pumped at 200 ml/min using a Gambro BMM-10 blood pump through a Hospal AN69HF haemofilter,. Measurements and results: Ten pharmacokinetic profiles were measured. The CVVHDF displayed a urea clearance of 42 +/- 3 ml/min, and removed ciprofloxacin with a clearance of 37 +/- 7 ml/min. This rate was 2-2.5 greater than previously published for ciprofloxacin in other forms of CRRT. On average the CVVHDF was responsible for clearing a fifth of all ciprofloxacin eliminated (21 +/- 10%). The total body clearance of ciprofloxacin was 12.2 +/- 4.3 l/h. The trough concentration following the initial dose was 0.7 +/- 0.3 mg/l. The area under the plasma concentration time curves over a 24-h period ranged from 21 to 55 mg .h l(-1). Conclusions: Intravenous ciprofloxacin 600 mg/day in critically ill patients using this form of CRRT produced adequate plasma levels for many resistant microbes found in intensive care units.

The design and implementation of a repository for the management of spatial data integrity constraints

This paper reviews the key features of an environment to support domain users in spatial information system (SIS) development. It presents a full design and prototype implementation of a repository system for the storage and management of metadata, focusing on a subset of spatial data integrity constraint classes. The system is designed to support spatial system development and customization by users within the domain that the system will operate.

Characterization of the highly efficient sucrose isomerase from Pantoea dispersa UQ68J and cloning of the sucrose isomerase gene

Sucrose isomerase (SI) genes from Pantoea dispersa UQ68J, Klebsiella planticola UQ14S, and Erwinia rhapontici WAC2928 were cloned and expressed in Escherichia coli. The predicted products of the UQ14S and WAC2928 genes were similar to known SIs. The UQ68J SI differed substantially, and it showed the highest isomaltulose-producing efficiency in E. coli cells. The purified recombinant WAC2928 SI was unstable, whereas purified UQ68J and UQ14S SIs were very stable. UQ68J SI activity was optimal at pH 5 and 30 to 35 degrees C, and it produced a high ratio of isomaltulose to trehalulose (> 22:1) across its pH and temperature ranges for activity (pH 4 to 7 and 20 to 50 degrees C). In contrast, UQ14S SI showed optimal activity at pH 6 and 35 degrees C and produced a lower ratio of isomaltulose to trehalulose (< 8:1) across its pH and temperature ranges for activity. UQ68J SI had much higher catalytic efficiency; the K-m was 39.9 mM, the V-max was 638 U mg(-1), and the K-cat/K-m was 1.79 x 104 M-1 s(-1), compared to a K-m of 76.0 mM, a V-max. of 423 U mg(-1), and a K-cat/K-m of 0.62 x 104 M-1 s(-1) for UQ14S SI. UQ68J SI also showed no apparent reverse reaction producing glucose, fructose, or trehalulose from isomaltulose. These properties of the P. dispersa UQ68J enzyme are exceptional among purified SIs, and they indicate likely differences in the mechanism at the enzyme active site. They may favor the production of isomaltulose as an inhibitor of competing microbes in high-sucrose environments, and they are likely to be highly beneficial for industrial production of isomaltulose.

A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.

On parameter estimation in population models

We describe methods for estimating the parameters of Markovian population processes in continuous time, thus increasing their utility in modelling real biological systems. A general approach, applicable to any finite-state continuous-time Markovian model, is presented, and this is specialised to a computationally more efficient method applicable to a class of models called density-dependent Markov population processes. We illustrate the versatility of both approaches by estimating the parameters of the stochastic SIS logistic model from simulated data. This model is also fitted to data from a population of Bay checkerspot butterfly (Euphydryas editha bayensis), allowing us to assess the viability of this population. (c) 2006 Elsevier Inc. All rights reserved.