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Flow cytometric DNA measurements yield the amount of DNA for each of a large number of cells. A DNA histogram normally consists of a mixture of one or more constellations of GdG,-, S-, G2/Mphase cells, together with internal standards, debris, background noise, and one or more populations of clumped cells. We have modelled typical DNA histograms as a mixed distribution with Gaussian densities for the Go/G1 and G2/M phases, an S-phase density, assumed to be uniform between the Go/G1 and G2/M peaks, observed with a Gaussian error, and with Gaussian densities for standards of chicken and trout red blood cells. The debris is modelled as a truncated exponential distribution, and we also have included a uniform background noise distribution over the whole observation interval. We have explored a new approach for maximum-likelihood analyses of complex DNA histograms by the application of the EM algorithm. This algorithm was used for four observed DNA histograms of varying complexity. Our results show that the algorithm works very well, and it converges to reasonable values for all parameters. In simulations from the estimated models, we have investigated bias, variance, and correlations of the estimates.Key terms: DNA-histogram analysis, maximum-likelihood estimation, cell-cycle compartments The DNA distribution, consisting of the Go/G1, S, and G2/M compartments of a cell population, provides useful information about the ploidy and the proliferation activity. These two indices, which express the modal DNA value and the total cell proliferation activity, respectively, of the cell population, have been measured in several investigations and shown to be of prognostic value in some malignancies (reviewed in 3,4). Flow cytometry (FCM) enables rapid quantification of DNA content of individual cells, giving the DNA distribution based on several thousand single cells in a couple of minutes (11,18,24,26,29,34). Therefore, FCM instruments have become important tools in producing raw data for the calculation of the ploidy and proliferation indices as well as other valuable cell characteristics.Many models and computer programs have been developed for the analysis of 9,[14][15][16][17][20][21][22]27,35), but most of these programs are limited to DNA histograms based on a cell population with just one DNA stemline and with DNA quantified with a resolution of 100-250 channels. In these cases, special efforts have been made to calculate the fraction of S-phase cells, particularly in synchronously growing cell cultures (41), but no attempt has been made to calculate the DNA index (DI) in these applications. The DI is here defined as the ratio between the modal Go/G1 DNA value of the cell population and a standard diploid peak (25). A comparison of various mathematical methods for DNA histogram analyses made by Baisch et al. (2) showed discrepancies in the estimates of the histogram compartments when the methods were applied to either a simulated histogram or a n experimentally derived DNA histogram based on a single cell stem line.Wit...

A hidden Markov regime is a Markov process that governs the time or space dependent distributions of an observed stochastic process. We propose a recursive algorithm for parameter estimation in a switching autoregressive process governed by a hidden Markov chain. A common approach to the recursive estimation problem is to base the estimation on suboptimal modifications of Kalman filtering techniques. The main idea in this paper is to use the maximum likelihood method and from this develop a recursive EM algorithm.

The Gaussian linear wave model, which has been successfully used in ocean engineering for more than half a century, is well understood, and there exist both exact theory and efficient numerical algorithms for calculation of the statistical distribution of wave characteristics. It is well suited for moderate seastates and deep water conditions. One drawback, however, is its lack of realism under extreme or shallow water conditions, in particular, its symmetry. It produces waves, which are stochastically symmetric, both in the vertical and in the horizontal direction. From that point of view, the Lagrangian wave model, which describes the horizontal and vertical movements of individual water particles, is more realistic. Its stochastic properties are much less known and have not been studied until quite recently. This paper presents a version of the first order stochastic Lagrange model that is able to generate irregular waves with both crest-trough and front-back asymmetries.