Generalized Mixability via Entropic Duality

Mixability is a property of a loss which characterizes when constant regret is possible in the game of prediction with expert advice. We show that a key property of mixability generalizes, and the $\exp$ and $\log$ operations present in the usual theory are not as special as one might have thought. In doing so we introduce a more general notion of $\Phi$-mixability where $\Phi$ is a general entropy (\ie, any convex function on probabilities). We show how a property shared by the convex dual of any such entropy yields a natural algorithm (the minimizer of a regret bound) which, analogous to the classical Aggregating Algorithm, is guaranteed a constant regret when used with $\Phi$-mixable losses. We characterize which $\Phi$ have non-trivial $\Phi$-mixable losses and relate $\Phi$-mixability and its associated Aggregating Algorithm to potential-based methods, a Blackwell-like condition, mirror descent, and risk measures from finance. We also define a notion of ``dominance'' between different entropies in terms of bounds they guarantee and conjecture that classical mixability gives optimal bounds, for which we provide some supporting empirical evidence

Phase shift effective range expansion from supersymmetric quantum mechanics

Supersymmetric or Darboux transformations are used to construct local phase equivalent deep and shallow potentials for $\ell \neq 0$ partial waves. We associate the value of the orbital angular momentum with the asymptotic form of the potential at infinity which allows us to introduce adequate long-distance transformations. The approach is shown to be effective in getting the correct phase shift effective range expansion. Applications are considered for the $^1P_1$ and $^1D_2$ partial waves of the neutron-proton scattering.Comment: 6 pages, 3 figures, Revtex4, version to be publised in Physical Review

Associations between blood sex steroid concentrations and risk of major adverse cardiovascular events in healthy older women in Australia: a prospective cohort substudy of the ASPREE trial

Background: Blood testosterone concentrations in women decline during the reproductive years and reach a nadir in the seventh decade, after which concentrations increase and are restored to those of reproductive-aged women early in the eighth decade. We aimed to establish the association between the concentration of testosterone in the blood and risk of major adverse cardiovascular events (MACE) and all-cause mortality in healthy older women. Methods: SHOW was a prospective cohort substudy of the longitudinal randomised ASPREE trial. Eligible participants were women aged at least 70 years from Australia with unimpaired cognition, no previous MACE, and a life expectancy of at least 5 years. Participants who were receiving hormonal or steroid therapy were ineligible for inclusion. We measured serum concentrations of sex steroids with liquid chromatography–tandem mass spectrometry and of SHBG with immunoassay. We compared lower concentrations of sex hormones with higher concentrations using four quartiles. Primary endpoints were risk of MACE and all-cause mortality, the associations of which with sex steroid concentrations were assessed using Cox proportional hazards regression that included age, body-mass index, smoking status, alcohol consumption, diabetes, hypertension, dyslipidaemia, impaired renal function, and treatment allocation in the ASPREE trial (aspirin vs placebo). ASPREE is registered with ClinicalTrials.gov, NCT01038583. Findings: Of the 9180 women recruited to the ASPREE trial between March 10, 2010, and Dec 31 2014, 6358 participants provided sufficient biobank samples at baseline and 5535 were included in the final analysis. Median age at entry was 74·0 years (IQR 71·7–77·7). During a median 4·4 years of follow-up (24 553 person-years), 144 (2·6%) women had a first MACE (incidence 5·9 per 1000 person-years). During a median 4·6 years of follow-up (3·8–5·6), 200 women died (7·9 per 1000 person-years). In the fully adjusted models, higher concentrations of testosterone were associated with a lower incidence of MACE (quartile 4 vs quartile 1: hazard ratio 0·57 [95% CI 0·36–0·91]; p=0·02), as were higher concentrations of DHEA (quartile 4 vs quartile 1: 0·61 [0·38–0·97]; p=0·04). For oestrone, a lower risk of MACE was seen for concentrations in quartile 2 only, compared with quartile 1 (0·55 [0·33–0·92]; p=0·02). In fully adjusted models, no association was seen between SHBG and MACE, or between any hormone or SHBG and all-cause mortality. Interpretation: Blood concentrations of testosterone and DHEA above the lowest quartile in older women were associated with a reduced risk of a first-ever MACE. Given that the physiological effects of DHEA are mediated through its steroid metabolites, if the current findings were to be replicated, trials investigating testosterone therapy for the primary prevention of ischaemic cardiovascular disease events in older women would be warranted. Funding: The National Health and Medical Research Council of Australia, US National Institute on Aging, the Victorian Cancer Agency, the Commonwealth Scientific and Industrial Research Organisation, and Monash University

A novel determination of the local dark matter density

We present a novel study on the problem of constructing mass models for the Milky Way, concentrating on features regarding the dark matter halo component. We have considered a variegated sample of dynamical observables for the Galaxy, including several results which have appeared recently, and studied a 7- or 8-dimensional parameter space - defining the Galaxy model - by implementing a Bayesian approach to the parameter estimation based on a Markov Chain Monte Carlo method. The main result of this analysis is a novel determination of the local dark matter halo density which, assuming spherical symmetry and either an Einasto or an NFW density profile is found to be around 0.39 GeV cm$^{-3}$ with a 1-$\sigma$ error bar of about 7%; more precisely we find a $\rho_{DM}(R_0) = 0.385 \pm 0.027 \rm GeV cm^{-3}$ for the Einasto profile and $\rho_{DM}(R_0) = 0.389 \pm 0.025 \rm GeV cm^{-3}$ for the NFW. This is in contrast to the standard assumption that $\rho_{DM}(R_0)$ is about 0.3 GeV cm$^{-3}$ with an uncertainty of a factor of 2 to 3. A very precise determination of the local halo density is very important for interpreting direct dark matter detection experiments. Indeed the results we produced, together with the recent accurate determination of the local circular velocity, should be very useful to considerably narrow astrophysical uncertainties on direct dark matter detection.Comment: 31 pages,11 figures; minor changes in the text; two figures adde

Dependence of direct detection signals on the WIMP velocity distribution

The signals expected in WIMP direct detection experiments depend on the ultra-local dark matter distribution. Observations probe the local density, circular speed and escape speed, while simulations find velocity distributions that deviate significantly from the standard Maxwellian distribution. We calculate the energy, time and direction dependence of the event rate for a range of velocity distributions motivated by recent observations and simulations, and also investigate the uncertainty in the determination of WIMP parameters. The dominant uncertainties are the systematic error in the local circular speed and whether or not the MW has a high density dark disc. In both cases there are substantial changes in the mean differential event rate and the annual modulation signal, and hence exclusion limits and determinations of the WIMP mass. The uncertainty in the shape of the halo velocity distribution is less important, however it leads to a 5% systematic error in the WIMP mass. The detailed direction dependence of the event rate is sensitive to the velocity distribution. However the numbers of events required to detect anisotropy and confirm the median recoil direction do not change substantially.Comment: 21 pages, 7 figures, v2 version to appear in JCAP, minor change