Using basis sets of scar functions

Using Piecewise Sinusoidal Basis Functions as Multiple Domain Basis Functions

This paper discusses application of the piecewise sinusoidal (PWS) basis function (BF) over a chain of several wire segments, i.e. as a multiple domain basis functions. The usage of PWS BF is compared to results based on the piecewise linear (PWL) basis functions. An example of meander monopole demonstrates the advantages associated with the PWS BF.

Numerical Solution of Singular IVPs of Lane-Emden Type Using Integral Operator and Radial Basis Functions

On fast computation of finite-time coherent sets using radial basis functions.

Finite-time coherent sets inhibit mixing over finite times. The most expensive part of the transfer operator approach to detecting coherent sets is the construction of the operator itself. We present a numerical method based on radial basis function collocation and apply it to a recent transfer operator construction [G. Froyland, "Dynamic isoperimetry and the geometry of Lagrangian coherent str...

Spatial Normalization using Basis Functions

This chapter describes the steps involved in registering images of different subjects into roughly the same co-ordinate system, where the co-ordinate system is defined by a template image (or series of images). The method only uses up to a few hundred parameters, so can only model global brain shape. It works by estimating the optimum coefficients for a set of bases, by minimizing the sum of sq...

Calculating response functions in time domain with nonorthonormal basis sets

We extend the recently proposed order-N algorithms for calculating linear- and nonlinear-response functions in time domain to the systems described by nonorthonormal basis sets.