Extinction times for a general birth, death and catastrophe process

The birth, death and catastrophe process is an extension of the birth-death process that incorporates the possibility of reductions in population of arbitrary size. We will consider a general form of this model in which the transition rates are allowed to depend on the current population size in an arbitrary manner. The linear case, where the transition rates are proportional to current population size, has been studied extensively. In particular, extinction probabilities, the expected time to extinction, and the distribution of the population size conditional on nonextinction (the quasi-stationary distribution) have all been evaluated explicitly. However, whilst these characteristics are of interest in the modelling and management of populations, processes with linear rate coefficients represent only a very limited class of models. We address this limitation by allowing for a wider range of catastrophic events. Despite this generalisation, explicit expressions can still be found for the expected extinction times.

Integrals for continuous-time Markov chains

This paper presents a method of evaluating the expected value of a path integral for a general Markov chain on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process. (C) 2002 Elsevier Science Inc. All rights reserved.

Uniting the nation? Disability, stem cells, and the Australian media

In this article, the 2002 Australian debate regarding embryonic stem cells is examined. This shows the importance of an analysis of the media to understanding how disability is constructed in discourses of nationhood and biotechnology. Media representation of disability-for instance, signifying disability as catastrophe-is seen as crucial in securing access to a variety of biotechnologies, such as embryonic stem cells. Analysis of such media moments shows a structure of privileged and excluded voices in debates regarding disability and biotechnology. The diversity of voices in the Australian community regarding disability is not represented in a range of media, nor are people with disability quoted as experts on disability. A recognition of the media's construction of disability must be matched by a commitment to disability as part of a truly civil society. It is only in this way that we will have biotechnologies, and diverse cultural and media representations that meet the requirements of the international disability rights movement motto of 'nothing about us without us', recently emphasized in the Disabled Peoples' International Europe's 2000 statement on biotechnology.

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.

Pattern-based reuse of successful designs: usability ofsafety-critical systems

Users of safety-critical systems are expected to effectively control or monitor complex systems, with errors potentially leading to catastrophe. For such systems, safety is of paramount importance and must be designed into the human-machine interface. While many case studies show how inadequate design practice led to poor safety and usability, concrete guidance on good design practices is scarce. The paper argues that the pattern language paradigm, widely used in the software design community, is a suitable means of documenting appropriate design strategies. We discuss how typical usability-related properties (e.g., flexibility) need some adjustment to be used for assessing safety-critical systems, and document a pattern language, based on corresponding "safety-usability" principles