Metrics for generalized persistence modules

We consider the question of defining interleaving metrics on generalized persistence modules over arbitrary preordered sets. Our constructions are functorial, which implies a form of stability for these metrics. We describe a large class of examples, inverse-image persistence modules, which occur whenever a topological space is mapped to a metric space. Several standard theories of persistence and their stability can be described in this framework. This includes the classical case of sublevelset persistent homology. We introduce a distinction between `soft' and `hard' stability theorems. While our treatment is direct and elementary, the approach can be explained abstractly in terms of monoidal functors.Comment: Final version; no changes from previous version. Published online Oct 2014 in Foundations of Computational Mathematics. Print version to appea

A re-appraisal of the fertility response to the Australian baby bonus

The Australian baby bonus offering parents $3,000 on the birth of a new child was announced on May 11 2004. The availability of five years of birth data following the introduction of the baby bonus allows for a more comprehensive analysis of the policy implications than is current in the literature. The focus of this paper is to identify if there is a positive fertility choice response to the introduction of the Australian baby bonus policy and if this response is sustained over time. To do this 19 years of birth and macroeconomic data, beginning 1990, is analysed using an unobservable components model. The results indicate a significant increase in birth numbers ten months following the announcement of the baby bonus, and this overall increase was sustained up to the end of the observed period. A cumulative growth in birth numbers which commenced in January 2006 slows in 2008 and 2009. It is suggested that the initial increase in births, identified in March 2005, is a direct fertility response to the introduction of the policy and that the subsequent change in the growth of birth numbers may be the result of a delayed effect working through a number of channels. It is estimated that approximately 119,000 births are attributable to the baby bonus over the period, at an approximate cost of$39000 per extra child.Fertility Rate, Time Series, baby bonus

Probing the Supersymmetric Inflaton and Dark Matter link via the CMB, LHC and XENON1T experiments

The primordial inflation dilutes all matter except the quantum fluctuations which we see in the cosmic microwave background (CMB) radiation. Therefore the last phases of inflation must be embedded within a beyond the Standard Model (SM) sector where the inflaton can directly excite the SM quarks and leptons. In this paper we consider two inflaton candidates LLe and udd whose decay can naturally excite all the relevant degrees of freedom besides thermalizing the lightest supersymmetric particle (LSP) during and after reheating. In particular, we present the regions of the parameter space which can yield successful inflation with the right temperature anisotropy in the CMB, the observed relic density for the neutralino LSP, and the recent Higgs mass constraints from LHC within the MSSM with non-universal Higgs masses -- referred to as the NUHM2 model. We found that in most scenarios, the LSP seems strongly mass degenerated with the next to lightest LSP (NLSP) and the branching ratio B_s -> mu^+ mu^- very close to the present bound, thus leading to falsifiable predictions. Also the dark matter interactions with XENON nuclei would fall within the projected range for the XENON1T experiment. In the case of a positive signal of low scale supersymmetry at the LHC, one would be able to potentially pin down the inflaton mass by using the associated values for the mass of the stau, the stop and the neutralino.Comment: 16 pages, 23 figures; v2: typos corrected; v3: version accepted by PR