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.

Composition and structure variation for magnetron sputtered tantalum oxynitride thin films, as function of deposition parameters

Tantalum oxynitride thin films were produced by magnetron sputtering. The films were deposited usinga pure Ta target and a working atmosphere with a constant N2/O2ratio. The choice of this constant ratiolimits the study concerning the influence of each reactive gas, but allows a deeper understanding of theaspects related to the affinity of Ta to the non-metallic elements and it is economically advantageous.This work begins by analysing the data obtained directly from the film deposition stage, followed bythe analysis of the morphology, composition and structure. For a better understanding regarding theinfluence of the deposition parameters, the analyses are presented by using the following criterion: thefilms were divided into two sets, one of them produced with grounded substrate holder and the otherwith a polarization of −50 V. Each one of these sets was produced with different partial pressure of thereactive gases P(N2+ O2). All the films exhibited a O/N ratio higher than the N/O ratio in the depositionchamber atmosphere. In the case of the films produced with grounded substrate holder, a strong increaseof the O content is observed, associated to the strong decrease of the N content, when P(N2+ O2) is higherthan 0.13 Pa. The higher Ta affinity for O strongly influences the structural evolution of the films. Grazingincidence X-ray diffraction showed that the lower partial pressure films were crystalline, while X-rayreflectivity studies found out that the density of the films depended on the deposition conditions: thehigher the gas pressure, the lower the density. Firstly, a dominant -Ta structure is observed, for lowP(N2+ O2); secondly a fcc-Ta(N,O) structure, for intermediate P(N2+ O2); thirdly, the films are amorphousfor the highest partial pressures. The comparison of the characteristics of both sets of produced TaNxOyfilms are explained, with detail, in the text.

Oxygen mass transfer impact on citric acid production by Yarrowia lipolytica from crude glycerol

Production of citric acid from crude glycerol from biodiesel industry, in batch cultures of Yarrowia lipolytica W29 was performed in a lab-scale stirred tank bioreactor in order to assess the effect of oxygen mass transfer rate in this bioprocess. An empirical correlation was proposed to describe oxygen volumetric mass transfer coefficient (kLa) as a function of operating conditions (stirring speed and specific air flow rate) and cellular density. kLa increased according with a power function with specific power input and superficial gas velocity, and slightly decreased with cellular density. The increase of initial kLa from 7 h-1 to 55 h-1 led to 7.8-fold increase of citric acid final concentration. Experiments were also performed at controlled dissolved oxygen (DO) and citric acid concentration increased with DO up to 60% of saturation. Thus, due to the simpler operation setting an optimal kLa than at controlled DO, it can be concluded that kLa is an adequate parameter for the optimization of citric acid production from crude glycerol by Y. lipolytica and to be considered in bioprocess scale-up. Our empirical correlation, considering the operating conditions and cellular density, will be a valid tool for this purpose.