Balanced algebraic unknotting, linking forms, and surfaces in three- and four-space

We provide three 3-dimensional characterizations of the Z-slice genus of a knot, the minimum genus of a locally-flat surface in 4-space cobounding the knot whose complement has cyclic fundamental group: in terms of balanced algebraic unknotting, in terms of Seifert surfaces, and in terms of presentation matrices of the Blanchfield pairing. This result generalizes to a knot in an integer homology 3-sphere and surfaces in certain simply connected signature zero 4-manifolds cobounding this homology sphere. Using the Blanchfield characterization, we obtain effective lower bounds for the Z-slice genus from the linking pairing of the double branched cover of the knot. In contrast, we show that for odd primes p, the linking pairing on the first homology of the p-fold branched cover is determined up to isometry by the action of the deck transformation group on said first homology.Comment: 39 pages, 5 figures, comments are welcome! v2: Added generalization of the main theorem to knots and surfaces in more general 3- and 4-manifolds; added new corollary showing equality of the Z-slice genus and the superslice genus; expanded introduction, and added example in last sectio

Smoothing ℓ1\ell_1-penalized estimators for high-dimensional time-course data

When a series of (related) linear models has to be estimated it is often appropriate to combine the different data-sets to construct more efficient estimators. We use $\ell_1$-penalized estimators like the Lasso or the Adaptive Lasso which can simultaneously do parameter estimation and model selection. We show that for a time-course of high-dimensional linear models the convergence rates of the Lasso and of the Adaptive Lasso can be improved by combining the different time-points in a suitable way. Moreover, the Adaptive Lasso still enjoys oracle properties and consistent variable selection. The finite sample properties of the proposed methods are illustrated on simulated data and on a real problem of motif finding in DNA sequences.Comment: Published in at http://dx.doi.org/10.1214/07-EJS103 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Discussion: One-step sparse estimates in nonconcave penalized likelihood models

Discussion of ``One-step sparse estimates in nonconcave penalized likelihood models'' [arXiv:0808.1012]Comment: Published in at http://dx.doi.org/10.1214/07-AOS0316A the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Impact of Aging on Future Healthcare Expenditure

The impact of aging on healthcare expenditure (HCE) has been at the center of a prolonged debate. This paper purports to shed light on several issues. First, it presents new evidence on the relative importance of the two components of HCE that have been distinguished by Zweifel, Felder and Meier (1999), viz. the cost of morbidity and the cost of mortality (their "red herring" hypothesis claims that neglecting the mortality component results in excessive estimates of future growth of HCE). Second, it takes account of recent evidence suggesting that HCE does increase life expectancy, implying that time-to-death is an endogenous determinant of HCE. Third, it investigates the contribution of population aging to the future growth of HCE. For the case of Switzerland, it finds this contribution to be relatively small regardless of whether or not the cost of dying is accounted for, thus qualifying the "red herring" hypothesis.Health econometrics, Aging, Cost of dying, Healthcare expenditure