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.     

ELECTRON SPIN RESONANCE THERMOMETRY APPLIED TO QUARTZITE COBBLES FROM VERGELEGEN SLAVE LODGE,SOMERSET WEST,SOUTH AFRICA

This paper describes the use of electron spin resonance spectroscopy to estimate the degree of heating of quartzite cobbles from hearths on the floor of the archaeological remains of an eighteenth-century Dutch colonial slave lodge. A novel technique based on the comparison of line intensities for the E’and O^-₂ centres in quartz distinguished successfully between cobbles which had been heated to estimated temperatures ranging from 300 °C to 450° C and controls from an adjacent stream bed. This inexpensive and simple technique could be applied to a wide range of archaeological problems involving the thermal history of objects consisting of or containing quartz.     

The culture history of Madagascar

Madagascar's culture is a unique fusion of elements drawn from the western, northern, and eastern shores of the Indian Ocean, and its past has fascinated many scholars, yet systematic archaeological research is relatively recent on the island. The oldest traces of visitors are from the first century AD. Coastal settlements, with clear evidence of ties to the western Indian Ocean trading network, were established in several places over the next millennium. Important environmental changes of both plant and animal communities are documented over this period, including the extinctions of almost all large animal species. Urban life in Madagascar began with the establishment of the entrepôt of Mahilaka on the northwest coast of the island in the twelfth century. At about the same time, communities with ties to the trade network were established around the island's coasts. From the fourteenth to the sixteenth century, social hierarchies developed in several regions of the island. During the succeeding two centuries, Madagascar saw the development of state polities.