Application of wavelets to the study of political history

\The idea that social processes develop in a cyclical manner is somewhat like a `Lorelei'. Researchers are lured to it because of its theoretical promise, only to become entangled in (if not wrecked by) messy problems of empirical inference. The reasoning leading to hypotheses of some kind of cycle is often elegant enough, yet the data from repeated observations rarely display the supposed cyclical pattern. (...) In addition, various `schools' seem to exist which frequently arrive at di erent conclusions on the basis of the same data." (van der Eijk and Weber 1987:271). Much of the empirical controversies around these issues arise because of three distinct problems: the coexistence of cycles of di erent periodicities, the possibility of transient cycles and the existence of cycles without xed periodicity. In some cases, there are no reasons to expect any of these phenomena to be relevant. Seasonality caused by Christmas is one such example (Wen 2002). In such cases, researchers mostly rely on spectral analysis and Auto-Regressive Moving-Average (ARMA) models to estimate the periodicity of cycles.1 However, and this is particularly true in social sciences, sometimes there are good theoretical reasons to expect irregular cycles. In such cases, \the identi cation of periodic movement in something like the vote is a daunting task all by itself. When a pendulum swings with an irregular beat (frequency), and the extent of the swing (amplitude) is not constant, mathematical functions like sine-waves are of no use."(Lebo and Norpoth 2007:73) In the past, this di culty has led to two di erent approaches. On the one hand, some researchers dismissed these methods altogether, relying on informal alternatives that do not meet rigorous standards of statistical inference. Goldstein (1985 and 1988), studying the severity of Great power wars is one such example. On the other hand, there are authors who transfer the assumptions of spectral analysis (and ARMA models) into fundamental assumptions about the nature of social phenomena. This type of argument was produced by Beck (1991) who, in a reply to Goldstein (1988), claimed that only \ xed period models are meaningful models of cyclic phenomena".We argue that wavelet analysis|a mathematical framework developed in the mid-1980s (Grossman and Morlet 1984; Goupillaud et al. 1984) | is a very viable alternative to study cycles in political time-series. It has the advantage of staying close to the frequency domain approach of spectral analysis while addressing its main limitations. Its principal contribution comes from estimating the spectral characteristics of a time-series as a function of time, thus revealing how its di erent periodic components may change over time. The rest of article proceeds as follows. In the section \Time-frequency Analysis", we study in some detail the continuous wavelet transform and compare its time-frequency properties with the more standard tool for that purpose, the windowed Fourier transform. In the section \The British Political Pendulum", we apply wavelet analysis to essentially the same data analyzed by Lebo and Norpoth (2007) and Merrill, Grofman and Brunell (2011) and try to provide a more nuanced answer to the same question discussed by these authors: do British electoral politics exhibit cycles? Finally, in the last section, we present a concise list of future directions.

Global vs. local nonlinear optimization techniques for human-like movement of an anthropomorphic robot

In this paper a comparison between using global and local optimization techniques for solving the problem of generating human-like arm and hand movements for an anthropomorphic dual arm robot is made. Although the objective function involved in each optimization problem is convex, there is no evidence that the admissible regions of these problems are convex sets. For the sequence of movements for which the numerical tests were done there were no significant differences between the optimal solutions obtained using the global and the local techniques. This suggests that the optimal solution obtained using the local solver is indeed a global solution.

Comparing heritage speakers and late L2-learners of European Portuguese: verb movement, VP ellipsis and adverb placement

This study compares the performance of Portuguese-German heritage children and adult L2 speakers of European Portuguese whose L1 is German with respect to two aspects of grammar, adverb placement and VP-ellipsis, which depend on a core syntactic property of the language, verb movement. The results show that both groups have acquired V-to-I and adverb placement, showing no influence of a V2 grammar. Performance in the VP-ellipsis task is more complex: heritage children produce VP-ellipsis at the level of controls, as opposed to L2 speakers; however, both L2 and heritage speakers show that crosslinguistic influence may produce a preference for pronoun substitution over VP-ellipsis in a task asking for redundancy resolution. Nevertheless, given that overall results show that heritage children perform at the level of L1 children, we take our results to support approaches to heritage bilingualism which suggest the development of an intact grammar in childhood.