We give a necessary condition for a meromorphic function in several variables to give rise to a Milnor fibration of the local link (respectively of the link at infinity). In the case of two variables we give some necessary and sufficient conditions for the local link (respectively the link at infinity) to be fibred.

Eigenspace models are a convenient way to represent sets of observations with widespread applications, including classification. In this paper we describe a new constructive method for incrementally adding observations to an eigenspace model. Our contribution is to explicitly account for a change in origin as well as a change in the number of eigenvectors needed in the basis set. No other metho...

This talk concerns when the complete graph on n vertices can be decomposed into d-dimensional cubes, where d is odd and n is even. (All other cases have been settled.) Necessary conditions are that n ≡ 1 (mod d) and n ≡ 0 (mod 2). These are known to be sufficient for d equal to 3 or 5, but for larger values of d a decomposition has been proven to exist for only sparce sets of n. We prove that f...

Networks based on basis set function expansions, such as the Radial Basis Function (RBF), or Separable Basis Function (SBF) networks, have non-linear parameters that are not trivial to optimize. Clustering techniques are frequently used to optimize positions for localized functions. Context-dependent fuzzy clustering techniques improve convergence of parameter optimization, leading to better ne...

There are multiple reasons why anisotropic basis functions may be needed or be more appropriate. The most obvious is that if the basis function is to be defined on Rn × T then there is no natural norm on this space that would reflect the unique properties of time. A second reason is that function being interpolated or approximated may incorporate a directional dependence. Thirdly, differentiabi...