A mathematical model for Escherichia coli debris size reduction during high pressure homogenisation based on grinding theory

Experimental data for E. coli debris size reduction during high-pressure homogenisation at 55 MPa are presented. A mathematical model based on grinding theory is developed to describe the data. The model is based on first-order breakage and compensation conditions. It does not require any assumption of a specified distribution for debris size and can be used given information on the initial size distribution of whole cells and the disruption efficiency during homogenisation. The number of homogeniser passes is incorporated into the model and used to describe the size reduction of non-induced stationary and induced E. coil cells during homogenisation. Regressing the results to the model equations gave an excellent fit to experimental data ( > 98.7% of variance explained for both fermentations), confirming the model's potential for predicting size reduction during high-pressure homogenisation. This study provides a means to optimise both homogenisation and disc-stack centrifugation conditions for recombinant product recovery. (C) 1997 Elsevier Science Ltd.

Risk Estimates of Dengue in Travelers to Dengue Endemic Areas Using Mathematical Models

Dengue has emerged as a frequent problem in international travelers. The risk depends on destination, duration, and season of travel. However, data to quantify the true risk for travelers to acquire dengue are lacking. We used mathematical models to estimate the risk of nonimmune persons to acquire dengue when traveling to Singapore. From the force of infection, we calculated the risk of dengue dependent on duration of stay and season of arrival. Our data highlight that the risk for nonimmune travelers to acquire dengue in Singapore is substantial but varies greatly with seasons and epidemic cycles. For instance, for a traveler who stays in Singapore for 1 week during the high dengue season in 2005, the risk of acquiring dengue was 0.17%, but it was only 0.00423% during the low season in a nonepidemic year such as 2002. Risk estimates based on mathematical modeling will help the travel medicine provider give better evidence-based advice for travelers to dengue endemic countries.

Developing logic programs from specifications using stepwise refinement

In this paper we demonstrate a refinement calculus for logic programs, which is a framework for developing logic programs from specifications. The paper is written in a tutorial-style, using a running example to illustrate how the refinement calculus is used to develop logic programs. The paper also presents an overview of some of the advanced features of the calculus, including the introduction of higher-order procedures and the refinement of abstract data types.