A Global Trend towards Democratic Convergence? A Lijphartian Analysis of Advanced Democracies.

The article offers a systematic analysis of the comparative trajectory of international democratic change. In particular, it focuses on the resulting convergence or divergence of political systems, borrowing from the literatures on institutional change and policy convergence. To this end, political-institutional data in line with Arend Lijphart’s (1999, 2012) empirical theory of democracy for 24 developed democracies between 1945 and 2010 are analyzed. Heteroscedastic multilevel models allow for directly modeling the development of the variance of types of democracy over time, revealing information about convergence, and adding substantial explanations. The findings indicate that there has been a trend away from extreme types of democracy in single cases, but no unconditional trend of convergence can be observed. However, there are conditional processes of convergence. In particular, economic globalization and the domestic veto structure interactively influence democratic convergence.

Remarks on the convergence of pseudospectra

We establish the convergence of pseudospectra in Hausdorff distance for closed operators acting in different Hilbert spaces and converging in the generalised norm resolvent sense. As an assumption, we exclude the case that the limiting operator has constant resolvent norm on an open set. We extend the class of operators for which it is known that the latter cannot happen by showing that if the resolvent norm is constant on an open set, then this constant is the global minimum. We present a number of examples exhibiting various resolvent norm behaviours and illustrating the applicability of this characterisation compared to known results.

SOP: Parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems

This paper presents a parallel surrogate-based global optimization method for computationally expensive objective functions that is more effective for larger numbers of processors. To reach this goal, we integrated concepts from multi-objective optimization and tabu search into, single objective, surrogate optimization. Our proposed derivative-free algorithm, called SOP, uses non-dominated sorting of points for which the expensive function has been previously evaluated. The two objectives are the expensive function value of the point and the minimum distance of the point to previously evaluated points. Based on the results of non-dominated sorting, P points from the sorted fronts are selected as centers from which many candidate points are generated by random perturbations. Based on surrogate approximation, the best candidate point is subsequently selected for expensive evaluation for each of the P centers, with simultaneous computation on P processors. Centers that previously did not generate good solutions are tabu with a given tenure. We show almost sure convergence of this algorithm under some conditions. The performance of SOP is compared with two RBF based methods. The test results show that SOP is an efficient method that can reduce time required to find a good near optimal solution. In a number of cases the efficiency of SOP is so good that SOP with 8 processors found an accurate answer in less wall-clock time than the other algorithms did with 32 processors.