Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Kinetic model for selective cultivation of microfungi in a microscreen process for food processing wastewater treatment and biomass production

The research was aimed at developing a technology to combine the production of useful microfungi with the treatment of wastewater from food processing. A recycle bioreactor equipped with a micro-screen was developed as a wastewater treatment system on a laboratory scale to contain a Rhizopus culture and maintain its dominance under non-aseptic conditions. Competitive growth of bacteria was observed, but this was minimised by manipulation of the solids retention time and the hydraulic retention time. Removal of about 90% of the waste organic material (as BOD) from the wastewater was achieved simultaneously. Since essentially all fungi are retained behind the 100 mum aperture screen, the solids retention time could be controlled by the rate of harvesting. The hydraulic retention time was employed to control the bacterial growth as the bacteria were washed through the screen at a short HRT. A steady state model was developed to determine these two parameters. This model predicts the effluent quality. Experimental work is still needed to determine the growth characteristics of the selected fungal species under optimum conditions (pH and temperature).

Reaching out to promote physical activity in Australia: A statewide randomized controlled trial of a stage-targeted intervention

Purpose. This study examined the broader use of a print-media intervention, which was previously shown to be effective at promoting physical activity to participants recruited from a regional Australian community, as a strategy suitable for a more diverse statewide Population sample. Methods. Participants were randomly selected adults who responded to a telephone interview conducted by the New South Wales Health Department and consented to Participate in a randomized controlled trial. Consenters were allocated to either intervention (n = 361) or control (n = 358) conditions. The intervention, a personalized letter plus stage-targeted booklets, was sent 1 week postbaseline. Data were collected via telephone inter view at baseline and 2 and 8 months and were analyzed using repeated measures analysis of variance (ANOVA) and chi(2) statistics. Results. The groups were similar at baseline (mean age 43 +/- 3 years; 64% women). Process evaluation showed high intervention recall (76% at 2 months) and high follow-up response rules (>85% at 8 months) were achieved. Nonsignificant increases in physical activity were observed (F-1,F-719 = 2.18, p =.14). Discussion. A single mailing of stage-targeted print materials was not effective in promoting increases in physical activity among participants selected from the statewide population. Future research could. examine how the effectiveness of print media might be enhanced, possibly by using supplementary media, community-based Prompts, or other incentives.

Accessing chain length dependent termination rate coefficients of methyl methacrylate (MMA) via the reversible addition fragmentation chain transfer (RAFT) process

The RAFT-CLD-T methodology is demonstrated to be not only applicable to 1-substituted monomers such as styrene and acrylates, but also to 1,1-disubstituted monomers such as MMA. The chain length of the terminating macromolecules is controlled by CPDB in MMA bulk free radical polymerization at 80 degrees C. The evolution of the chain length dependent termination rate coefficient, k(t)(i,i), was constructed in a step-wise fashion, since the MMA/CPDB system displays hybrid behavior (between conventional and living free radical polymerization) resulting in initial high molecular weight polymers formed at low RAFT agent concentrations. The obtained CLD of k(t) in MMA polymerizations is compatible with the composite model for chain length dependent termination. For the initial chain-length regime, up to a degree of polymerization of 100, k(t) decreases with alpha (in the expression k(t)(i,i) = k(t)(0) . i(-alpha)) being close to 0.65 at 80 degrees C. At chain lengths exceeding 100, the decrease is less pronounced (affording an alpha of 0.15 at 80 degrees C). However, the data are best represented by a continuously decreasing nonlinear functionality implying a chain length dependent alpha.

Controlled oxidative protein refolding using an ion-exchange column

Column-based refolding of complex and highly disulfide-bonded proteins simplifies protein renaturation at both preparative and process scale by integrating and automating a number of operations commonly used in dilution refolding. Bovine serum albumin (BSA) was used as a model protein for refolding and oxido-shuffling on an ion-exchange column to give a refolding yield of 55 % after 40 Ih incubation. Successful on-column refolding was conducted at protein concentrations of up to 10 mg/ml and refolded protein, purified from misfolded forms, was eluted directly from the column at a concentration of 3 mg/ml. This technique integrates the dithiothreitol removal, refolding, concentration and purification steps, achieving a high level of process simplification and automation, and a significant saving in reagent costs when scaled. Importantly, the current result suggests that it is possible to controllably refold disulfide-bonded proteins using common and inexpensive matrices, and that it is not always necessary to control protein-surface interactions using affinity tags and expensive chromatographic matrices. Moreover, it is possible to strictly control the oxidative refolding environment once denatured protein is bound to the ion-exchange column, thus allowing precisely controlled oxido-shuffling. (c) 2005 Elsevier B.V. All rights reserved.

Extinction times for a birth-death process with two phases

Many populations have a negative impact on their habitat or upon other species in the environment if their numbers become too large. For this reason they are often subjected to some form of control. One common control regime is the reduction regime: when the population reaches a certain threshold it is controlled (for example culled) until it falls below a lower predefined level. The natural model for such a controlled population is a birth-death process with two phases, the phase determining which of two distinct sets of birth and death rates governs the process. We present formulae for the probability of extinction and the expected time to extinction, and discuss several applications. (c) 2006 Elsevier Inc. All rights reserved.