Fertility and Social Security

The data show that an increase in government provided old-age pensions is strongly correlated with a reduction in fertility. What type of model is consistent with this finding? We explore this question using two models of fertility: one by Barro and Becker (1989), and one inspired by Caldwell (1978, 1982) and developed by Boldrin and Jones (2002). In Barro and Becker's model parents have children because they perceive their children's lives as a continuation of their own. In Boldrin and Jones' framework parents procreate because children care about their parents' utility, and thus provide them with old-age transfers. The effect of increases in government provided pensions on fertility in the Barro and Becker model is very small, whereas the effect on fertility in the Boldrin and Jones model is sizeable and accounts for between 55 and 65% of the observed Europe-U.S. fertility differences both across countries and across time.Social security ; Financial markets

Revealing the tidal scars of the Small Magellanic Cloud

Due to their close proximity, the Large and Small Magellanic Clouds (SMC/LMC) provide natural laboratories for understanding how galaxies form and evolve. With the goal of determining the structure and dynamical state of the SMC, we present new spectroscopic data for $\sim$ 3000 SMC red giant branch stars observed using the AAOmega spectrograph at the Anglo-Australian Telescope. We complement our data with further spectroscopic measurements from previous studies that used the same instrumental configuration and proper motions from the \textit{Gaia} Data Release 2 catalogue. Analysing the photometric and stellar kinematic data, we find that the SMC centre of mass presents a conspicuous offset from the velocity centre of its associated \mbox{H\,{\sc i}} gas, suggesting that the SMC gas is likely to be far from dynamical equilibrium. Furthermore, we find evidence that the SMC is currently undergoing tidal disruption by the LMC within 2\,kpc of the centre of the SMC, and possibly all the way in to the very core. This is evidenced by a net outward motion of stars from the SMC centre along the direction towards the LMC and apparent tangential anisotropy at all radii. The latter is expected if the SMC is undergoing significiant tidal stripping, as we demonstrate using a suite of $N$-body simulations of the SMC/LMC system disrupting around the Milky Way. These results suggest that dynamical models for the SMC that assume a steady state will need to be revisited.Comment: Revised version submitted to MNRAS after referee report, 18 pages, 18 figure

On the stochastic mechanics of the free relativistic particle

Given a positive energy solution of the Klein-Gordon equation, the motion of the free, spinless, relativistic particle is described in a fixed Lorentz frame by a Markov diffusion process with non-constant diffusion coefficient. Proper time is an increasing stochastic process and we derive a probabilistic generalization of the equation $(d\tau)^2=-\frac{1}{c^2}dX_{\nu}dX_{\nu}$. A random time-change transformation provides the bridge between the $t$ and the $\tau$ domain. In the $\tau$ domain, we obtain an \M^4-valued Markov process with singular and constant diffusion coefficient. The square modulus of the Klein-Gordon solution is an invariant, non integrable density for this Markov process. It satisfies a relativistically covariant continuity equation

Scaling of dynamics with the range of interaction in short-range attractive colloids

We numerically study the dependence of the dynamics on the range of interaction $\Delta$ for the short-range square well potential. We find that, for small $\Delta$, dynamics scale exactly in the same way as thermodynamics, both for Newtonian and Brownian microscopic dynamics. For interaction ranges from a few percent down to the Baxter limit, the relative location of the attractive glass line and the liquid-gas line does not depend on $\Delta$. This proves that in this class of potentials, disordered arrested states (gels) can be generated only as a result of a kinetically arrested phase separation.Comment: 4 pages, 4 figure

Non-universal Voronoi cell shapes in amorphous ellipsoid packings

In particulate systems with short-range interactions, such as granular matter or simple fluids, local structure plays a pivotal role in determining the macroscopic physical properties. Here, we analyse local structure metrics derived from the Voronoi diagram of configurations of oblate ellipsoids, for various aspect ratios $\alpha$ and global volume fractions $\phi_g$. We focus on jammed static configurations of frictional ellipsoids, obtained by tomographic imaging and by discrete element method simulations. In particular, we consider the local packing fraction $\phi_l$, defined as the particle's volume divided by its Voronoi cell volume. We find that the probability $P(\phi_l)$ for a Voronoi cell to have a given local packing fraction shows the same scaling behaviour as function of $\phi_g$ as observed for random sphere packs. Surprisingly, this scaling behaviour is further found to be independent of the particle aspect ratio. By contrast, the typical Voronoi cell shape, quantified by the Minkowski tensor anisotropy index $\beta=\beta_0^{2,0}$, points towards a significant difference between random packings of spheres and those of oblate ellipsoids. While the average cell shape $\beta$ of all cells with a given value of $\phi_l$ is very similar in dense and loose jammed sphere packings, the structure of dense and loose ellipsoid packings differs substantially such that this does not hold true. This non-universality has implications for our understanding of jamming of aspherical particles.Comment: 6 pages, 5 figure

Exploring the spectroscopic diversity of type Ia supernovae with DRACULA: a machine learning approach

The existence of multiple subclasses of type Ia supernovae (SNeIa) has been the subject of great debate in the last decade. One major challenge inevitably met when trying to infer the existence of one or more subclasses is the time consuming, and subjective, process of subclass definition. In this work, we show how machine learning tools facilitate identification of subtypes of SNeIa through the establishment of a hierarchical group structure in the continuous space of spectral diversity formed by these objects. Using Deep Learning, we were capable of performing such identification in a 4 dimensional feature space (+1 for time evolution), while the standard Principal Component Analysis barely achieves similar results using 15 principal components. This is evidence that the progenitor system and the explosion mechanism can be described by a small number of initial physical parameters. As a proof of concept, we show that our results are in close agreement with a previously suggested classification scheme and that our proposed method can grasp the main spectral features behind the definition of such subtypes. This allows the confirmation of the velocity of lines as a first order effect in the determination of SNIa subtypes, followed by 91bg-like events. Given the expected data deluge in the forthcoming years, our proposed approach is essential to allow a quick and statistically coherent identification of SNeIa subtypes (and outliers). All tools used in this work were made publicly available in the Python package Dimensionality Reduction And Clustering for Unsupervised Learning in Astronomy (DRACULA) and can be found within COINtoolbox (https://github.com/COINtoolbox/DRACULA).Comment: 16 pages, 12 figures, accepted for publication in MNRA

A study of the 't Hooft loop in SU(2) Yang-Mills theory

We study the behaviour of the spatial and temporal 't Hooft loop at zero and finite temperature in the 4D SU(2) Yang-Mills theory, using a new numerical method. In the deconfined phase $T>T_c$, the spatial 't Hooft loop exhibits a dual string tension, which vanishes at $T_c$ with 3D Ising-like critical exponent.Comment: 4 pages, 5 figures. Version accepted for publication in Phys. Rev. Let