A database of number fields

We describe an online database of number fields which accompanies this paper The database centers on complete lists of number fields with prescribed invariants. Our description here focuses on summarizing tables and connections to theoretical issues of current interest.Comment: 25 pages, 1 figur

Sick of work or too sick to work? Evidence on health shocks and early retirement from the BHPS

We follow individuals as they retire using discrete-time hazard models applied to a stock sample from 12 waves of the British Household Panel Survey. Results confirm that health shocks are a determinant of retirement age and are quantitatively more important than pension entitlement. This is the case for both men and women and is observed for both a measure of health limitations and a measure of latent health status obtained from a generalized ordered probit model. Further, our results provide evidence that, for women, the health status of their partner impacts on their retirement decisions; an effect that is not evident for men

Early Retirement and Inequality in Britain and Germany: How Important Is Health?

Both health and income inequalities have been shown to be much greater in Britain than in Germany. One of the main reasons seems to be the difference in the relative position of the retired, who, in Britain, are much more concentrated in the lower income groups. Inequality analysis reveals that while the distribution of health shocks is more concentrated among those on low incomes in Britain, early retirement is more concentrated among those on high incomes. In contrast, in Germany, both health shocks and early retirement are more concentrated among those with low incomes. We use comparable longitudinal data sets from Britain and Germany to estimate hazard models of the effect of health on early retirement. The hazard models show that health is a key determinant of the retirement hazard for both men and women in Britain and Germany. The size of the health effect appears large compared to the other variables. Designing financial incentives to encourage people to work for longer may not be sufficient as a policy tool if people are leaving the labour market involuntarily due to health problems.health, early retirement, hazard models

The tame-wild principle for discriminant relations for number fields

Consider tuples of separable algebras over a common local or global number field, related to each other by specified resolvent constructions. Under the assumption that all ramification is tame, simple group-theoretic calculations give best possible divisibility relations among the discriminants. We show that for many resolvent constructions, these divisibility relations continue to hold even in the presence of wild ramification.Comment: 31 pages, 11 figures. Version 2 fixes a normalization error: |G| is corrected to n in Section 7.5. Version 3 fixes an off-by-one error in Section 6.

Face and voice attractiveness judgments change during adolescence

Attractivenessjudgments are thought to underpin adaptive mate choice decisions. We investigated how these judgmentschange during adolescence when mate choice is becoming relevant. Adolescents aged 11–15 evaluated faces and voices manipulated along dimensions that affect adults' judgments of attractiveness and that are thought to cue mate value. Facial stimuli consisted of pairs of faces that were more or less average, more or less feminine, or more or less symmetric. The adolescents selected the more average, symmetric, and feminine faces as more attractive more often than chance, but judgments of some facial traits differed significantly with rater age and sex, indicating a role of development in judgments of facial cues. Vocal stimuli consisted of pairs of voices manipulated to raise or lower perceived pitch. The older but not younger girls selected the lower-pitched male voices as more attractive at rates above chance, while the younger but not older boys selected the higher-pitched female voices as more attractive. Controlling for rater age, increased pubertal development was associated with increased selection of lower-pitched boys' voices by girls and decreased selection of feminized male faces by boys. Our results are the first to demonstrate that adolescents show somewhat similar attractivenessjudgments to adults in age-matched stimuli and that age, sex, and pubertal development have measurable effects on adolescents' attractivenessjudgments. They suggest that attractivenessjudgments in humans, at least for some traits, are facultatively calibrated to the individual's life stage, only reaching adult values upon sexual maturity when mate choice decisions become relevant

Mixed mode oscillations in a conceptual climate model

Much work has been done on relaxation oscillations and other simple oscillators in conceptual climate models. However, the oscillatory patterns in climate data are often more complicated than what can be described by such mechanisms. This paper examines complex oscillatory behavior in climate data through the lens of mixed-mode oscillations. As a case study, a conceptual climate model with governing equations for global mean temperature, atmospheric carbon, and oceanic carbon is analyzed. The nondimensionalized model is a fast/slow system with one fast variable (corresponding to ice volume) and two slow variables (corresponding to the two carbon stores). Geometric singular perturbation theory is used to demonstrate the existence of a folded node singularity. A parameter regime is found in which (singular) trajectories that pass through the folded node are returned to the singular funnel in the limiting case where $\epsilon = 0$. In this parameter regime, the model has a stable periodic orbit of type $1^s$ for some $s>0$. To our knowledge, it is the first conceptual climate model demonstrated to have the capability to produce an MMO pattern.Comment: 28 pages, 11 figure

Voice pitch preferences of adolescents: Do changes across time indicate a shift towards potentially adaptive adult-like preferences?

An evolutionary approach to attractiveness judgments emphasises that many human trait preferences exist in order to assist adaptive mate choice. Here we test an adaptive development hypothesis, whereby voice pitch preferences indicating potential mate quality might arise or strengthen significantly during adolescence (when mate choice becomes adaptive). We used a longitudinal study of 250 adolescents to investigate changes in preference for voice pitch, a proposed marker of mate quality. We found significantly stronger preferences for lower-pitched opposite-sex voices in the older age group compared with the younger age group (using different sets of age-matched stimuli), and marginally increased preferences for lower-pitched opposite-sex voices comparing within-participant preferences for the same set of stimuli over the course of 1 year. We also found stability in individual differences in preferences across adolescence: controlling for age, the raters who had stronger preferences than their peers for lower pitched voices when first tested, retained stronger preferences for lower-pitched voices relative to their peers about 1 year later. Adolescence provides a useful arena for evaluating adaptive hypotheses and testing the cues that might give rise to adaptive behaviour