Fluctuation analysis, which is often used to demonstrate random mutagenesis in cell lines (and to estimate mutation rates), is based on the properties of a probability distribution known as the Luria-Delbrück distribution (and its generalizations). The two main new results reported in this paper are (i) a simple, completely general, and computationally efficient procedure for calculating probability distributions arising from fluctuation analysis and (ii) the formula for this procedure when cells in a colony have only grown for a finite number of generations after initial seeding. It is also shown that the procedure reduces to one that was developed earlier when an infinite number of generations is assumed. The derivation of the generating function of the distribution is also clarified. The results obtained should also be useful to experimentalists when only a relatively short time elapses between seeding and harvesting cultures for fluctuation analysis.

The Luria–Delbrück distribution arises in birth-and-mutation processes in population genetics that have been systematically studied for the last fifty years. The central result reported in this paper is a new recursion relation for computing this distribution which supersedes all past results in simplicity and computational efficiency: p 0 = e–m ; where m is the expected number of mutations. A new relation for the asymptotic behavior of pn (≈ c/n 2) is also derived. This corresponds to the probability of finding a very large number of mutants. A formula for the z-transform of the distribution is also reported.

Nonstationary signals with finite time support are frequently encountered in electrophysiology and other fields of biomedical research. It is often desirable to have a compact description of their shape and of their time evolution. For this purpose, Fourier analysis is not necessarily the best tool. The Hermite-Rodriguez and Associated Hermite basis functions are applied in this work. Both are based on the product of Hermite polynomials and Gaussian functions. Their general properties relevant to biomedical signal processing are reviewed. Preliminary applications are described concerning the analysis and description of: a) test signals such as a square pulse and a single cycle of a sinewave, b) electrically evoked myoelectric signals, and c) power spectra of either voluntary or evoked signals. It is shown that expansions with only five to ten terms provide an excellent description of the computer simulated and real signals. It is shown that these two families of Hermite functions are well suited for the analysis of nonstationary biological evoked potentials with compact time support. An application to the estimation of scaling factors of electrically evoked myoelectric signals is described. The Hermite functions show advantages with respect to the more traditional spectral analysis, especially in the case of signal truncation due to stimulation with interpulse intervals smaller than the duration of the evoked response. Finally, the Hermite approach is found to be suitable for classification of spectral shapes and compression of spectral information of either voluntary or evoked signals. The approach is very promising for neuromuscular diagnosis and assessment because of its capability for information compression and waveform classification.

most cases has been evaluated incorrectly in the past. For example, there is no formal justification for the approximations due to Jokipii (1966, 1971), which permit this integral to be expressed simply in terms of a one-dimensional power spectrum of magnetic field fluctuations, evaluated at a resonant wavenumber. By using both analytic and numerical techniques, we correctly evaluate <(AP2) >/At for a general form of the power spectrum, which should provide a good fit to observed power spectra. In the limit of low rigidity, where the ratio of the correlation length for field fluctuations to the particle's gyro-radius is large,,the correct result for <(Ap) 2 >/At differs from that due to Jokipii (1966) by a factor of p (for p 0).At all but very small values of p, this correction will introduce only a small numerical change in predicted values of <(AP) 2 >/At. However, in certain schemes for averaging <(Ap) 2 >/At over p, and for, forming the diffusion coefficient for propagation parallel to the mean field (Jokipii, 1966(Jokipii, , 1971Earl, 1973), this extra factor of p introduces strong divergences as P-0.These divergences no doubt result from the inadequacies near p=0 of the quasi-linear and adiabatic approximations. We also show that quasi-linear/adiabatic theory does not in general predict that <(Ap) 2 >/At =0 at p =0 (e.g. Jokipii, 1966(e.g. Jokipii, , 1971 or that <(Ap) 2 >/At diverges continuously to infinity as p-*0 (Hasselmann and Wibberenz, 1968). Rather, this theory predicts for physically realistic power spectra that < (Ap) 2 >/At contains a delta-function, 6 (p). Finally, we discuss how the above corrections affect our ability to determine an accurate diffusion coefficient for propagation parallel to the mean

The Luria–Delbrück distribution arises in birth-and-mutation processes in population genetics that have been systematically studied for the last fifty years. The central result reported in this paper is a new recursion relation for computing this distribution which supersedes all past results in simplicity and computational efficiency: p0 = e–m; where m is the expected number of mutations. A new relation for the asymptotic behavior of pn (≈ c/n2) is also derived. This corresponds to the probability of finding a very large number of mutants. A formula for the z-transform of the distribution is also reported.