Let K be a closed, normal cone with nonempty interior int(K) in a Banach space X. Let Σ = {x ∈ int(K) : q(x) = 1} where q: int(K) → (0,∞) is continuous and homogeneous of degree 1 and it is usually assumed that Σ is bounded in norm. In this framework there is a complete metric d, Hilbert’s projective metric, defined on Σ and a complete metric d, Thompson’s metric, defined on int(K). We study pr...

Subset currents on hyperbolic groups were introduced by Kapovich and Nagnibeda as a generalization of geodesic groups, which Bonahon have been successfully studied in the case fundamental group <mml:...

Abstract. Let A = P +K be an n×n complex matrix with P = 1 2 (A−HAH) and K = 1 2 (A+ HAH), H being a unitary involution. Having characterised all unitary involutions, we investigate the spectral structure of P and K and, in particular, characterise the eigenvalues of K as zeros of a rational function and prove that, for normal A, σ(K) resides in the convex hull of σ(A). We also demonstrate that...

In many application areas, it is important to detect outliers. The traditional engineering approach to outlier detection is that we start with some “normal” values x1, . . . , xn, compute the sample average E, the sample standard deviation σ, and then mark a value x as an outlier if x is outside the k0sigma interval [E − k0 · σ,E + k0 · σ] (for some pre-selected parameter k0). In real life, we ...

Let F = (Kn,P) be a circulant homogeneous factorisation of index k, that means P is a partition of the arc set of the complete digraph Kn into k circulant factor digraphs such that there exists σ ∈ Sn permuting the factor circulants transitively amongst themselves. Suppose further such an element σ normalises the cyclic regular automorphism group of these circulant factor digraphs, we say F is ...

We consider problems in finite-sample inference with two-step, monotone incomplete data drawn from Nd(μ,Σ), a multivariate normal population with mean μ and covariance matrix Σ. We derive a stochastic representation for the exact distribution of b μ, the maximum likelihood estimator of μ. We obtain ellipsoidal confidence regions for μ through T , a generalization of Hotelling’s statistic. We de...

In many application areas, it is important to detect outliers. The traditional engineering approach to outlier detection is that we start with some “normal” values x1, . . . , xn, compute the sample average E, the sample standard variation σ, and then mark a value x as an outlier if x is outside the k0-sigma interval [E − k0 · σ, E + k0 · σ] (for some pre-selected parameter k0). In real life, w...

The datum σ yields a measure dσ on the boundary ∂P—on each edge E we take dσ to be a constant multiple of the standard Lebesgue measure with the constant normalised so that the mass of the edge is σ(E). Equally, the datum σ specifies an affine-linear defining function λE for each edge E, i.e. the edge lies in the hyperplane λ E (0). We choose an inward-pointing normal vector v at a point of E w...

abstract scaling methods, which are based on similar media theory, are used to simplify the statistic description of soil spatial variations. to simulate the water flow in heterogeneous soils, simultaneous scaling of soil hydraulic functions, including soil water retention and unsaturated hydraulic conductivity functions, is highly desirable. in the similar media theory, the simultaneous scalin...