Gravity-Type Interactive Markov Models—Part II: Lyapunov Stability of Steady States

In Part I of this paper (Smith and Hsieh, 1997) a programming formulation of steady states was developed for gravity-type interactive Markov chains in terms of their associated spatial-flow chains. These results are here applied to analyze the stability properties of interactive Markov chains. In particular, the objective function for this programming formulation is shown to constitute a Lyapunov function for an appropriately defined continuous-time version of spatial-flow chains. The Lyapunov stability properties of these spatial flows are then shown to yield corresponding stability properties for the continuous-time versions of interactive Markov chains. In particular, these processes always exhibit global convergence to steady states. Finally, it is shown that when steady states are unique, these convergence results are inherited by those interactive Markov chains that are 'sufficiently close' to their continuous-time versions.     

Claiming the high ground: theories of imperial authority and the British hill stations in India

By the 1880s, imperial government's practice of ‘retreating’ to the Indian hill stations for much of the year was well established. Despite the strength of this new tradition, such a relocation of colonial administration never lacked its critics. This paper examines the expanding administrative use of the hill stations from the early nineteenth century through the 1880s. As the nineteenth century ‘scientific’ framework for British control of India was formed, conflicting strategies and practices for maintaining imperial control required mediation and contrasting frameworks for defining duty and loyalty between government and subject vied for dominance. The significance of Utilitarian thought, changing appraisals of climate and constructions of race are evaluated in an analysis of the imperial hill stations.