The Landau electron problem on a cylinder

We consider the quantum mechanics of an electron confined to move on an infinite cylinder in the presence of a uniform radial magnetic field. This problem is in certain ways very similar to the corresponding problem on the infinite plane. Unlike the plane however, the group of symmetries of the magnetic field, namely, rotations about the axis and the axial translations, is {\em not} realized by the quantum electron but only a subgroup comprising rotations and discrete translations along the axial direction, is. The basic step size of discrete translations is such that the flux through the `unit cylinder cell' is quantized in units of the flux quantum. The result is derived in two different ways: using the condition of projective realization of symmetry groups and using the more familiar approach of determining the symmetries of a given Hamiltonian.Comment: 26 pages, revtex file, no figures. In version 2, introduction is expanded to explain our approach and references are updated. Results and conclusions are unchange

Family Unification from Universality

A direct consequence of the occurrence of fermion families is the invariance of currents under certain groups of (universality) transformations. We show how these universality groups can themselves be used to find and study grand family unification models. Identifying two independent - weak and strong - universality groups and assuming that the grand unification group is SU(8N), its subgroup respecting either weak or strong universality is shown to be G = SU(2)xU(1)xSU(3). The fundamental representation of SU(8N) decomposes as N families of leptons and quarks. In the G-invariant limit, all fermions are left-handed. A mechanism for generating the correct number of right-handed fermions with the correct couplings so as to give pure vector colour and electromagnetic currents is exhibited. Universality is shown to result most naturally from a preonic structure of fermions. In such a preonic picture there are no ultraheavy gauge bosons and no anomaly or hierarchy problem.Comment: 30 page

Prediction of disability-free survival in healthy older people

AbstractProlonging survival in good health is a fundamental societal goal. However, the leading determinants of disability-free survival in healthy older people have not been well established. Data from ASPREE, a bi-national placebo-controlled trial of aspirin with 4.7 years median follow-up, was analysed. At enrolment, participants were healthy and without prior cardiovascular events, dementia or persistent physical disability. Disability-free survival outcome was defined as absence of dementia, persistent disability or death. Selection of potential predictors from amongst 25 biomedical, psychosocial and lifestyle variables including recognized geriatric risk factors, utilizing a machine-learning approach. Separate models were developed for men and women. The selected predictors were evaluated in a multivariable Cox proportional hazards model and validated internally by bootstrapping. We included 19,114 Australian and US participants aged ≥65 years (median 74 years, IQR 71.6–77.7). Common predictors of a worse prognosis in both sexes included higher age, lower Modified Mini-Mental State Examination score, lower gait speed, lower grip strength and abnormal (low or elevated) body mass index. Additional risk factors for men included current smoking, and abnormal eGFR. In women, diabetes and depression were additional predictors. The biased-corrected areas under the receiver operating characteristic curves for the final prognostic models at 5 years were 0.72 for men and 0.75 for women. Final models showed good calibration between the observed and predicted risks. We developed a prediction model in which age, cognitive function and gait speed were the strongest predictors of disability-free survival in healthy older people.Trial registrationClinicaltrials.gov (NCT01038583)</jats:p