In this work an R-tree variant, which uses minimum volume covering ellipsoids instead of usual minimum bounding rectangles, is presented. The most significant aspects, which determine R-tree index structure performance, is an amount of dead space coverage and overlaps among the covering regions. Intuitively, ellipsoid as a quadratic surface should cover data more tightly, leading to less dead s...

The use of realistic FE head models in EIT of brain function confers significant advantages, but image quality is critically dependent on mesh geometrical integrity. Generation of accurate models for individual subjects is time-consuming, so warping an existing idealised mesh to closely approximate specific patient geometry is being investigated. The head was modelled as an ellipsoid to obtain ...

In this paper, Banach space duality theory for the multiobjective H 2 / H m problem developed recently by the authors, is used to develop algorithms to solve this problem by approximately reducing the dual and predual reperesentations to finite variable convex optimizations. The Ellipsoid algorithm is then a p plied to these problems to obtain polynomial-time, nonheuristic programs which find “...

The algorithm proposed in this paper runs in a polynomial oracle time, i.e., in a number of arithmetic operations and calls to the separation oracle bounded by a polynomial in the number of variables and in the maximum binary size of an entry of the coefficient matrix. This algorithm is much simpler than traditional polynomial algorithms such as the ellipsoid method and the volumetric barrier m...

Set-membership algorithms, including the conventional optimal bounding ellipsoid (OBE) algorithm, require a priori knowledge of exact error bounds which is unknown in most applications. Conservative (over-estimated) error bounds used in practice lead to inconsistent parameter estimation. The novel OBE algorithm with automatic bound estimation (OBE-ABE) is shown to be consistently convergent wit...

In this paper, a novel model of elliptical basis function neural networks (EBFNN) is proposed. Firstly, a geometry analytic algorithm is applied to construct the hyper-ellipsoid units of hidden layer of the EBFNN, i.e., an initial structure of the EBFNN, which is further pruned by the particle swarm optimization (PSO) algorithm. Finally, the experimental results demonstrated the proposed hybrid...

A new approach to address constrained robust regulation for systems with a polytopic uncertainty description is proposed. The infinite horizon state feedback-law is represented by a sequence of explicit control laws that corresponds to a sequence of asymptotically invariant ellipsoids constructed off-line one within another. Beginning with the smallest ellipsoid each subsequent one (and the cor...

Veech groups uniformize Teichmüller geodesics in Riemann moduli space. We gave examples of infinitely generated Veech groups; see Duke Math. J. 123 (2004), 49–69. Here we show that the associated Teichmüller geodesics can even have both infinitely many cusps and infinitely many infinite ends.

This paper proposes a variant of the normalized cut algorithm for spectral clustering. Although the normalized cut algorithm applies the K-means algorithm to the eigenvectors of a normalized graph Laplacian for finding clusters, our algorithm instead uses a minimum volume enclosing ellipsoid for them. We show that the algorithm shares similarity with the ellipsoidal rounding algorithm for separ...