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Hermite polynomials and Hermite functions are used for constructing infinite-band filterbanks for perfect reconstruction (PR). The analysis filters and the synthesis filterbanks give PR for a large class of signals possessing infinite bandwidth.

A wavelet-based neural network for developing models or functions from training data is introduced. The network has a similar architecture to radial basis (RBF) function network, except that the radial basis functions are replaced by orthonormal scaling functions. A consistent function estimator, it has universal and L(sup 2) approximation characteristics which render its performance comparable to that of the multi-layer perceptrons and RBF networks.

A wave-based expansion series analogous to Karhunen-Loeve expansion for wide-sense stationary methods does not involve eigenequation solutions and time-restriction conditions. The new series is more advantageous than the Fourier series and contains no correlated coefficients. The fundamental functions for the series are derived from power spectral density and Lemaire-Meyer type wavelets.

Partially edited molecules for the cytochrome-c oxidase subunit III (CO III) transcript from two species of the insect trypanosome Herpetomonas were examined. In 24 to 61 partially edited clones, editing is not restricted only 3' to 5'. The editing process possibly evolved slowly because the area of base pairing between individual guide RNAs and the COIII transcript is not strictly consumed in kinetoplastids.

The theory of chromatic derivatives leads to chromatic series which replace Taylor's series for bandlimited functions. For such functions, these series have a global convergence property not shared by Taylor's series. In this work the theory is extended to bandlimited functions of slow growth. This includes many signals of practical importance such as polynomials, periodic functions and almost periodic functions. This extension also enables us to get improved local convergence results for chromatic series. [ABSTRACT FROM AUTHOR]

Chromatic series are series expansions in which the coefficients are linear combinations of derivatives of a function. They were introduced by Ignjatovic (Introduction to Signal Processing Based on Differential Operators, Tech. Rep. 1, Kromos Technology, available at http://www.kromos.com, February 2001.) as a replacement for Taylor's series and are based on orthogonal polynomials. However, real data usually involves the values of a function and not its derivatives which are needed in both theories. In this article, we replace the derivatives by discrete values in the calculations of the coefficients. [ABSTRACT FROM AUTHOR]

Slepian functions (Prolate Spheroidal Wave Functions) are obtained by maximizing the energy of a σ-bandlimiled function (nonnalized with total energy I) on a prescribed ititen'al [ -τ τ]. The solution to this problem leads to an eigenvalue problem λf(t) = ∫τ-τ{sinσ(t - x)/π(t - x)}f(x)dx, whose solutions, in turn, form an orthogonal sequence {ϕn}. This sequence is a basis of the Paley-Wiener space Bσ of σ-bandlimited functions. For σ = π, integer translates of the Slepian functions of order 0, {ϕ0(t - n)} form a Riesz basis of the same space. Furthermore, by using ϕ0, as a scaling function we can construct a wavelet theory based on them. Two methods of density estimations thus naturally arise; one based on the orthogonal system {ϕn} and the other on the scaling functions {ϕ0(t - n)}. The former gives more rapid convergence, while the latter avoids Gibbs phenomenon, is locally positive, and allows the use of thresholding methods. Both approaches exhibit a strong localization property. [ABSTRACT FROM AUTHOR]

Presents a method for recovering a computed tomography image from its sampled projections. Recovery of the image in the form of values of the Radon transform; Use of the properties of the raised-cosine wavelet in recovering the image; Rate of convergence of the resulting algorithm to the image density function.

We study the distribution of exons in eukaryotic genes to determine whether one can detect the reuse of exon sequences and to use the frequency of such reuse to estimate how many ancestral exon sequences there might have been. We use two databases of exons. One contained 56,276 internal exons from putatively unrelated genes (less than 20% sequence identity) and the second contained 8917 internal exons from regions of these genes that are homologous and colinear with prokaryotic genes; these are ancient conserved regions (ACRs). At the 95% significance level we find 3500 exon-sequence matches in the large database and 500 matches in the ACR database. These matches correspond to groups of similar sequences. The size–rank relationship for these groups follows a power law, the size falling off as the inverse square root of the rank. This form of the power law distribution leads us to make an estimate for the size of a possible universe of ancestral exons. Using the data corresponding to the ACR regions, that universe is estimated to be about 15,000–30,000 in size. [ABSTRACT FROM AUTHOR]

Gibbs phenomenon occurs for most approximations based on standard orthogonal expansions, as well as for those based on integral operators. It also occurs in interpolations and other types of approximations. We consider a general approach to approximation based on delta sequences in an attempt to better understand the concept. [ABSTRACT FROM AUTHOR]