The accuracy of a diagnostic test is typically characterised using the receiver operating characteristic (ROC) curve. Summarising indexes such as the area under the ROC curve (AUC) are used to compare different tests as well as to measure the difference between two populations. Often additional information is available on some of the covariates which are known to influence the accuracy of such ...

On a space of stable maps, the psi classes are modified by subtracting certain boundary divisors. The top products of modified psi classes, usual psi classes, and classes pulled back along the evaluation maps are called twisted descendants; it is shown that in genus 0, they admit a complete recursion and are determined by the Gromov-Witten invariants. One motivation for this construction is tha...

Let k = Fq(t) be the rational function field with finite constant field and characteristic p ≥ 3, and let K/k be a finite separable extension. For a fixed place v of k and an elliptic curveE/K which has ordinary reduction at all places ofK extending v, we consider a canonical height pairing 〈 , 〉v : E(K ) × E(K) → C v which is symmetric, bilinear and Galois equivariant. The pairing 〈 , 〉∞ for t...

Let Fg 1, g> 1, be the mapping class group consisting of all isotopy classes of base-point and orientation preserving homeomorphisms of a closed, oriented surface F of genus g. Let )~(~1) be its Euler characteristic in the sense of Wall, that is Z(F~I)= [Fgl: F] l z(E/F), where F is any torsion free subgroup of finite index in F~ 1 and E is a contractible space on which F acts freely and proper...

The receiver operating characteristic (ROC) curve displays the capacity of a marker or diagnostic test to discriminate between two groups of subjects, cases versus controls. We present a comprehensive suite of Stata commands for performing ROC analysis. Non-parametric, semiparametric and parametric estimators are calculated. Comparisons between curves are based on the area or partial area under...

We give a formula for the Sn-equivariant Euler characteristics of the moduli spaces Mg,n of genus g curves with n marked points.

Let k be a field of positive characteristic p. Question: Does every twisted form of μp over k occur as subgroup scheme of an elliptic curve over k? We show that this is true for most finite fields, for local fields and for fields of characteristic p ≤ 11. However, it is false in general for fields of characteristic p ≥ 13, which is related to the fact that the Igusa curves are not rational in t...

• M , the equivalent of a single time step, if we explore the curves for a given (t, τ). Examples of this are shown using LIC images throughout the paper, for example Figures 7d and 7e. Furthermore, this case applies to advected stream surfaces for a given (t, τ) such as the one shown in Figure 9. It shall be noted that the pre-computed ̄̄ q can be used to compute all advected stream surfaces for...

This paper presents a novel surface modelling scheme to construct a freeform surface progressively from unorganised curves representing the boundary and interior characteristic curves. The approach can construct a base surface model from four ordinary or composite boundary curves and support incremental surface updating from interior characteristic curves, some of which may not be on the final ...

In a famous 1967 paper [ŠT], Šafarevič and Tate constructed elliptic curves of arbitrarily large rank r over rational function fields of positive characteristic. The group of rational points of such a curve yields a lattice in Euclidean space of dimension r via the canonical Néron-Tate height. It seems natural to investigate the structure of this lattice, but curiously it was not until about 19...