Automatic and semi-automatic magnetic resonance angiog-raphy (MRA) segmentation techniques can potentially save radiologists large amounts of time required for manual segmentation and can facilitate further data analysis. The proposed MRA segmentation method uses a mathematical modeling technique which is well-suited to the complicated curve-like structure of blood vessels. We deene the segment...

A technique of descent via 4-isogeny is developed on the Jacobian of a curve of genus 2 of the form: Y 2 = q1(X)q2(X)q3(X), where each qi(X) is a quadratic defined over Q. The technique offers a realistic prospect of calculating rank tables of Mordell-Weil groups in higher dimension. A selection of worked examples is included as illustration.

In 1989 Happel conjectured that for a finite-dimensional algebra A over an algebraically closed field k, gl.dim.A < ∞ if and only if hch.dim.A < ∞. Recently Buchweitz-Green-Madsen-Solberg gave a counterexample to Happel’s conjecture. They found a family of pathological algebra Aq for which gl.dim.Aq = ∞ but hch.dim.Aq = 2. These algebras are pathological in many aspects, however their Hochschil...

In the PAC Model we assume there exists a distribution D on the examples X that the learner receives, i.e., when choosing an instance from the sample it is drawn according to D. We assume that D is: 1. Fixed throughout the learning process. 2. Unknown to the learner. 3. The instances are chosen independently. The target concept is specified as a computable function c, thus our instances are of ...