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.

Assessment of the effects of the expansion of the city of Estarreja on the rational land use

The management of urban environment, together with the preservation of the natural environment and the creation of a sustainable built environment, is a complex challenge for contemporary societies. In the name of progress, cities are contributing for the degradation of all surrounding ecosystems. Therefore there is an arising demand for developing new strategies and a new urban development paradigm settled in the search for the equilibrium between natural and built environments and efficient use of resources. The objective of this paper is to analyse how the urban expansion of the city of Estarreja took place in relation to the land use, based on the land capability classification maps of the area. Based in the results some sustainable development strategies that might be applied to the city are discussed. The obtained results demonstrate that the city has been growing faster then its population, consuming vast portions of land, since its growth as been occurring in a linear form. Despite this fact, results show that most of this expansion took place towards a territory of lower agricultural potential, when comparing to the location of its original settlement.

Characterization of late antique and early medieval pottery production of the city of Braga and its territory

The fundamental goal we set ourselves when developing this study is to try to characterize, both technically and formally, ceramics made in the city of Braga and its territory from the initial moments of the Late Antiquity to the Middle Ages. Thus, we will focus on analyzing some own productions that appear attached to the phases of late antique occupation —ceramics of red engobes and late gray—, as well as in the early medieval containers identified in different archaeological interventions practiced in the Braga environment. Concretely, we will analyze the material from various excavations conducted recently at the Theatre in the solar number 20/28 and 36/56 from the Afonso Henriques Street and the former District Hostel as well as the church of São Martinho de Dume.