Ronald K. Pearson

Robust detection of periodic time series measured from biological systems

BackgroundPeriodic phenomena are widespread in biology. The problem of finding periodicity in biological time series can be viewed as a multiple hypothesis testing of the spectral content of a given time series. The exact noise characteristics are unknown in many bioinformatics applications. Furthermore, the observed time series can exhibit other non-idealities, such as outliers, short length and distortion from the original wave form. Hence, the computational methods should preferably be robust against such anomalies in the data.ResultsWe propose a general-purpose robust testing procedure for finding periodic sequences in multiple time series data. The proposed method is based on a robust spectral estimator which is incorporated into the hypothesis testing framework using a so-called g-statistic together with correction for multiple testing. This results in a robust testing procedure which is insensitive to heavy contamination of outliers, missing-values, short time series, nonlinear distortions, and is completely insensitive to any monotone nonlinear distortions. The performance of the methods is evaluated by performing extensive simulations. In addition, we compare the proposed method with another recent statistical signal detection estimator that uses Fishers test, based on the Gaussian noise assumption. The results demonstrate that the proposed robust method provides remarkably better robustness properties. Moreover, the performance of the proposed method is preferable also in the standard Gaussian case. We validate the performance of the proposed method on real data on which the method performs very favorably.ConclusionAs the time series measured from biological systems are usually short and prone to contain different kinds of non-idealities, we are very optimistic about the multitude of possible applications for our proposed robust statistical periodicity detection method.AvailabilityThe presented methods have been implemented in Matlab and in R. Codes are available on request. Supplementary material is available at: http://www.cs.tut.fi/sgn/csb/robustperiodic/.

Estimation and inversion of the effects of cell population asynchrony in gene expression time-series

We introduce several approaches to improve the quality of gene expression data obtained from time-series measurements by applying signal processing tools. Performance of the proposed methods are examined using both simulated and real yeast gene expression data. In particular, we concentrate especially on a smoothing effect caused by the distribution of the cell population in time and introduce several methods for inverting this phenomenon. The proposed methods can be used to significantly improve the accuracy of the gene expression time-series measurements since the cell population asynchrony (wide distribution) is inevitably caused by the different operation pace of the cells. Some of the proposed methods rely on the partition of the genes, as well as the corresponding expression profiles, into the cell cycle regulated and noncell cycle regulated genes. For that purpose, we first study the cell cycle regulated genes and introduce a method that can be used to estimate the period length of those genes. We also estimate the spreading rate of the underlying distribution of the cell population based solely on the observed gene expression data. After the preliminary experiments, we introduce some methods for estimating the underlying distribution of the cell population instead of its spreading rate. These methods assume certain additional measurements, such as flow cytometry (e.g. fluorescent-activated cell sorter (FACS)) or bud counting measurements, to be available. We also apply the standard blind deconvolution method for estimating the true distribution of the cell population. The found estimates of the spreading rate of the cell distribution and the distributions of the cell population themself are used to invert the smoothing effect. To that end, we discuss some inversion approaches applicable to the problem in hand.

Scale-invariant nonlinear digital filters

Many signal processing applications involve procedures with simple, known dependences on positive rescalings of the input data; examples include correlation and spectral analysis, quadratic time-frequency distributions, and coherence analysis. Often, system performance can be improved with pre- and/or post-processing procedures, and one of the advantages of linear procedures (e.g., smoothing and sharpening filters) is their scale-invariance (x/sub k//spl rarr/y/sub k/ implies /spl lambda/x/sub k//spl rarr//spl lambda/y/sub k/). There are, however, important cases where linear processing is inadequate, motivating interest in nonlinear digital filters. This paper considers the general problem of designing nonlinear filters that exhibit the following scaling behavior: x/sub k//spl rarr/y/sub k/ implies /spl lambda/x/sub k//spl rarr//spl lambda//sup /spl nu//y/sub k/ for some /spl nu/>0, with particular emphasis on the case v=1. Results are presented for two general design approaches. The first is the top-down design of these filters, in which a relatively weak structural constraint is imposed (e.g., membership in the nonlinear FIR class), and a complete characterization is sought for all filters satisfying the scaling criterion for some fixed /spl nu/. The second approach is the bottom-up design of filters satisfying specified scaling behavior by interconnecting simpler filter structures with known scaling behavior. Examples are presented to illustrate both the simplicity and the utility of these design approaches.

CONTROL-RELEVANT CHARACTERIZATION OF NONLINEAR CLASSES OF PROCESS SYSTEMS

Abstract In this work, a nonlinearity measure is used to examine the relative severity of various classes of inherently nonlinear behavior. Using the Optimal Control Structure, the analysis includes a study of how the classes and their properties affect systems control-relevant nonlinearity. Two chemical reactor systems that demonstrate a wide range of nonlinear behaviors are examined. The results indicate that the nonlinearity measure is able to distinguish between the different categories of nonlinear behavior. The control-relevant analysis indicates that the open-loop behavior may or may not necessarily transfer to the control-relevant setting.