Birth-death processes with mass annihilation and state-dependent immigration

A birth-death process is subject to mass annihilation at rate β with subsequent mass immigration occurring into state j at rateα j . This structure enables the process to jump from one sector of state space to another one (via state 0) with transition rate independent of population size. First, we highlight the difficulties encountered when using standard techniques to construct both time-dependent and equilibrium probabilities. Then we show how to overcome such analytic difficulties by means of a tool developed in Chen and Renshaw (1990, 1993b); this approach is applicable to many processes whose underlying generator on E\{0} has known probability structure. Here we demonstrate the technique through application to the linear birth-death generator on which is superimposed an annihilation/immigration process.

Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration

Attention has recently focussed on stochastic population processes that can undergo total annihilation followed by immigration into state j at rate αj. The investigation of such models, called Markov branching processes with instantaneous immigration (MBPII), involves the study of existence and recurrence properties. However, results developed to date are generally opaque, and so the primary motivation of this paper is to construct conditions that are far easier to apply in practice. These turn out to be identical to the conditions for positive recurrence, which are very easy to check. We obtain, as a consequence, the surprising result that any MBPII that exists is ergodic, and so must possess an equilibrium distribution. These results are then extended to more general MBPII, and we show how to construct the associated equilibrium distributions.

Matching case history patterns in case-based reasoning

This paper introduces a mechanism for representing and recognizing case history patterns with rich internal temporal aspects. A case history is characterized as a collection of elemental cases as in conventional case-based reasoning systems, together with the corresponding temporal constraints that can be relative and/or with absolute values. A graphical representation for case histories is proposed as a directed, partially weighted and labeled simple graph. In terms of such a graphical representation, an eigen-decomposition graph matching algorithm is proposed for recognizing case history patterns.

An introduction to China's rail transport Part 1: History, present and future of China's railways

In this paper an introduction is given to the history, current situation and future plans of China's railway industry. The history of China's railway is divided into four development phases: the phase in Imperial China, the phase in the Republic of China and the phases before and after the economic rejuvenation of the People's Republic of China. An introduction to the current situation and future plans includes the major projects under construction and development trends of China's railways. The environment of China's railways is also presented. This is the first of two papers on the railway scene in China.

BSHM meetings: BMS History of Mathematics Splinter Group

Introduction to abstracts from papers given at BMS History of Mathematics Splinter Group, held 17 April 2007, in Swansea.

[BSHM meetings] Topics in the history of financial mathematics: early commerce to chaos in modern stock markets

This account provides an overview of the study day, entitled 'Topics in the History of Financial Mathematics: Early commerce to chaos in modern stock markets,' held by the British Society for the History of Mathematics jointly with Gresham College, at Gresham College, London on 25th April 2008. The series of talks explored the development of mathematics and mathematical techniques in a commercial and financial context.

Reality-experiential history documentaries: the Trench (BBC, 2002) and Britain's modern memory of the First World War

Culloden (BBC, 1964) The Great War (BBC, 1964) 1914-18 (BBC/KCET, 1996) Haig: the Unknown Soldier (BBC, 1996) Veterans: the Last Survivors of the Great War (BBC, 1998) 1900s House (Channel 4, 1999) The Western Front (BBC, 1999) History of Britain (BBC, 2000) 1940s House (Channel 4, 2001) The Ship (BBC, 2002) Surviving the Iron Age (BBC, 2001) The Trench (BBC, 2002) Frontier House (Channel 4, 2002) Lad's Army (BBC, 2002) Edwardian Country House (Channel 4, 2002) Spitfire Ace (Channel 4, 2003) World War One in Colour (Channel 5, 2003) 1914: the War Revolution (BBC, 2003) The First World War (Channel 4, 2003) Dunkirk (BBC, 2004) Dunkirk: The Soldier's Story (BBC, 2004) D-Day to Berlin (BBC, 2004) Bad Lad's Army (ITV, 2004) Destination D-Day: Raw Recruits (BBC, 2004) Bomber Crew (Channel 4, 2004) Battlefield Britain (BBC, 2004) The Last Battle (ARTE/ZDF, 2005) Who Do You Think You Are? (BBC, 2004, 2006) The Somme (Channel 4, 2005) [From the Publisher]