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.     

Quaker Schoolmasters, Toleration and the Law, 1689–1714

The 1689 Toleration Act allowed Protestant dissenters freedom to worship in public, but it was only a limited toleration and dissenters continued to suffer discrimination. This article examines the experience of Quakers in one important area, the Anglican monopoly in teaching. Although the prosecution of unlicensed teachers was patchy, localised, and dependent upon the hostility and zeal of particular individuals, few dissenters escaped harassment. Moreover, Friends appear to have suffered more severely because of the particular dislike that they still provoked and their unwillingness to compromise which often led to imprisonment. The growth in High Church feeling during Anne's reign led to a more rigorous enforcement of the existing statutes and the passing of the Schism Act (1714). The consequences of an Anglican educational monopoly have not been properly considered by historians largely from the assumption that the Schism Act was fatally compromised by the death of Queen Anne, and because little attention has been paid to the continued harassment of dissenters after toleration who attempted to teach. The Schism Act was repealed in 1719, but freedom for Quakers and other dissenters to teach had already been achieved largely through the courts.     

A Little Bit of Dirt

An examination of the surface deposit of an Etruscan cup said to have been dug up in Cheshire suggests instead that it had been buried in Italy and brought to England in recent times. The method described here might usefully be employed to assess the provenance of buried artefacts.     

COINTEGRATION BETWEEN U.S. WHEAT MARKETS

ABSTRACT. Average monthly price data from twelve hinterland markets and the Houston port price for wheat are studied in a cointegration framework using the Engle-Granger "two-step" procedure and Johansen's maximum likelihood procedure. Out-of-sample forecasts from an error correction model are compared to those from a vector autoregression fit to levels and a univariate autoregression fit to first differences. This comparison suggests that modeling these (cointegrated) data as a levels vector autoregression, rather than as an error-correction process, results in significantly higher error bias, but lower error variance, at long horizons.     

Peace Protest and Policy

The tremendous fluctuations in public mobilization against United States nuclear weapons policy, a relatively stable policy over four decades, present a difficult riddle to social scientists. Since the dawn of the nuclear age small groups of activists have consistently protested both the content of United States national security policy and the process by which it is made. Only occasionally, however, has this protest spread beyond a handful of relatively marginal groups, generated substantial public support, and reached mainstream political institutions. This article examines the political cycles of peace movement engagement and quiescence, and their relation to external political context, particularly public policy. I begin with a brief review of the relevant literature on the origins of the movements, noting parallels in the study of interest groups. Building on recent literature on political opportunity structure. I suggest a theoretical framework which emphasizes the interaction between activists choices and political context. I then describe the cycles of peace movement activism and quiescence on nuclear weapons issues in the United States using mass media sources to delineate periods of mobilization. I outline a number of policy variables which may help explain protest mobilization. My conclusions address the importance of policy and political context in explaining movement cycles and the potential influence of protest movements on policy.