Polynomial expansion

Explicit Polynomial Expansion

The Zeckendorf Expansion of Polynomial Sequences

In the first part of the paper we prove that the Zeckendorf sum-ofdigits function sZ(n) and similarly defined functions evaluated on polynomial sequences of positive integers or primes satisfy a central limit theorem. We also prove that the Zeckendorf expansion and the q-ary expansions of integers are asymptotically independent.

Polynomial expansion for orientation and motion estimation

This thesis introduces a new signal transform, called polynomial expansion, and based on this develops novel methods for estimation of orientation and motion. The methods are designed exclusively in the spatial domain and can be used for signals of any dimensionality. Two important concepts in the use of the spatial domain for signal processing is projections into subspaces, e.g. the subspace o...

Polynomial chaos expansion of a multimodal random vector

A methodology and algorithms are proposed for constructing the polynomial chaos expansion (PCE) of multimodal random vectors. An algorithm is developed for generating independent realizations of any multimodal multivariate probability measure that is constructed from a set of independent realizations using the Gaussian kernel-density estimation method. The PCE is then performed with respect to ...

A Subset Expansion of the Coloured Tutte Polynomial

Bollobás and Riordan introduce a Tutte polynomial for coloured graphs and matroids in [3]. We observe that this polynomial has an expansion as a sum indexed by the subsets of the ground-set of a coloured matroid, generalizing the subset expansion of the Tutte polynomial. We also discuss similar expansions of other contraction–deletion invariants of graphs and matroids. 1. The coloured Tutte pol...