New biorthogonal potential--density basis functions

We use the weighted integral form of spherical Bessel functions, and introduce a new analytical set of complete and biorthogonal potential--density basis functions. The potential and density functions of the new set have finite central values and they fall off, respectively, similar to $r^{-(1+l)}$ and $r^{-(4+l)}$ at large radii where $l$ is the latitudinal quantum number of spherical harmonics. The lowest order term associated with $l=0$ is the perfect sphere of de Zeeuw. Our basis functions are intrinsically suitable for the modeling of three dimensional, soft-centred stellar systems and they complement the basis sets of Clutton-Brock, Hernquist & Ostriker and Zhao. We test the performance of our functions by expanding the density and potential profiles of some spherical and oblate galaxy models.Comment: 8 pages, 6 figures, Accepted for publication in Monthly Notices of the Royal Astronomical Societ

Generalised cosine functions, basis and regularity properties

We examine regularity and basis properties of the family of rescaled $p$-cosine functions. We find sharp estimates for their Fourier coefficients. We then determine two thresholds, $p_02$, such that this family is a Schauder basis of $L_s(0,1)$ for all $s>1$ and $p\in[p_0,p_1]$.Comment: 24 page

Regularized system identification using orthonormal basis functions

Most of existing results on regularized system identification focus on regularized impulse response estimation. Since the impulse response model is a special case of orthonormal basis functions, it is interesting to consider if it is possible to tackle the regularized system identification using more compact orthonormal basis functions. In this paper, we explore two possibilities. First, we construct reproducing kernel Hilbert space of impulse responses by orthonormal basis functions and then use the induced reproducing kernel for the regularized impulse response estimation. Second, we extend the regularization method from impulse response estimation to the more general orthonormal basis functions estimation. For both cases, the poles of the basis functions are treated as hyperparameters and estimated by empirical Bayes method. Then we further show that the former is a special case of the latter, and more specifically, the former is equivalent to ridge regression of the coefficients of the orthonormal basis functions.Comment: 6 pages, final submission of an contribution for European Control Conference 2015, uploaded on March 20, 201

Wideband Characteristic Basis Functions in Radiation Problems

In this paper, the use of characteristic basis function (CBF) method, augmented by the application of asymptotic waveform evaluation (AWE) technique is analyzed in the context of the application to radiation problems. Both conventional and wideband CBFs are applied to the analysis of wire and planar antennas

Building Adaptive Basis Functions with a Continuous SOM

This paper introduces CSOM, a distributed version of the Self-Organizing Map network capable of generating maps similar to those created with the original algorithm. Due to the continuous nature of the mapping, CSOM outperforms the traditional SOM algorithm in function approximation tasks. System performance is illustrated with three examples