BACKGROUND: Over the past decade, many investigators have used sophisticated time series tools for the analysis of genomic sequences. Specifically, the correlation of the nucleotide chain has been studied by examining the properties of the power spectrum. The main limitation of the power spectrum is that it is restricted to stationary time series. However, it has been observed over the past decade that genomic sequences exhibit non-stationary statistical behavior. Standard statistical tests have been used to verify that the genomic sequences are indeed not stationary. More recent analysis of genomic data has relied on time-varying power spectral methods to capture the statistical characteristics of genomic sequences. Techniques such as the evolutionary spectrum and evolutionary periodogram have been successful in extracting the time-varying correlation structure. The main difficulty in using time-varying spectral methods is that they are extremely unstable. Large deviations in the correlation structure results from very minor perturbations in the genomic data and experimental procedure. A fundamental new approach is needed in order to provide a stable platform for the non-stationary statistical analysis of genomic sequences. RESULTS: In this paper, we propose to model non-stationary genomic sequences by a time-dependent autoregressive moving average (TD-ARMA) process. The model is based on a classical ARMA process whose coefficients are allowed to vary with time. A series expansion of the time-varying coefficients is used to form a generalized Yule-Walker-type system of equations. A recursive least-squares algorithm is subsequently used to estimate the time-dependent coefficients of the model. The non-stationary parameters estimated are used as a basis for statistical inference and biophysical interpretation of genomic data. In particular, we rely on the TD-ARMA model of genomic sequences to investigate the statistical properties and differentiate between coding and non-coding regions in the nucleotide chain. Specifically, we define a quantitative measure of randomness to assess how far a process deviates from white noise. Our simulation results on various gene sequences show that both the coding and non-coding regions are non-random. However, coding sequences are "whiter" than non-coding sequences as attested by a higher index of randomness. CONCLUSION: We demonstrate that the proposed TD-ARMA model can be used to provide a stable time series tool for the analysis of non-stationary genomic sequences. The estimated time-varying coefficients are used to define an index of randomness, in order to assess the statistical correlations in coding and non-coding DNA sequences. It turns out that the statistical differences between coding and non-coding sequences are more subtle than previously thought using stationary analysis tools: Both coding and non-coding sequences exhibit statistical correlations, with the coding regions being "whiter" than the non-coding regions. These results corroborate the evolutionary periodogram analysis of genomic sequences and revoke the stationary analysis' conclusion that coding DNA behaves like random sequences.

The human pupillary light reflex has long been studied as a typical biological nonlinear system. We have used a sinusoidal non-harmonic signal as the input light stimulus and pupil diameter as the output of the system. A recursive least square method is then used to estimate the measured pupil diameter in terms of the input light. With a good estimate, the underlying dynamical behavior of the system would be captured by the estimated parameters. Thus we modeled the estimated parameters as ARIMA processes. Then the residual noise associated with the ARIMA models was examined and revealed that people with narcolepsy had considerably lower sum-square-error than people without this sleep disorder (controls). This method turns out to be a relatively simple and fast test procedure for narcolepsy discrimination.

A model of an asset market with noiseless price feedback is shown to achieve maximum profits for the market traders and also to achieve a point on the rate distortion function of the market input. A simplified version of the model, which is empirically more robust than the original, is shown to be a market operating with a fixed signal power. For this version it is found that there is a tradeoff between trader profits and price distortion. Unlike a pure communication channel, the market has its mutual information set by informed traders to maximize expected profits rather than set to minimize distortion. It is found that expected profits are maximized when there is just the right amount of price distortion.

This paper presents several adaptive linear predictive coding techniques based upon extension of recursive ladder filters to two and three dimensions (2-D/3-D). A 2-D quarter-plane autoregressive ladder filter is developed using a least square criterion in an exact recursive fashion. The 2-D recursive ladder filter is extended to a 3-D case which can adaptively track the variation of both spatial and temporal changes of moving images. Using the 2-D/3-D ladder filters and a previous frame predictor, two types of adaptive predictor-control schemes are proposed in which the prediction error at each pel can be obtained at or close to a minimum level. We also investigate several modifications of the basic encoding methods. Performance of the 2D/3-D ladder filters, their adaptive control schemes, and variations in coding methods are evaluated by computer simulations on two real sequences and compared to the results of motion compensation and frame differential coders. As a validity test of the ladder filters developed, the error signals for the different predictors are compared and the visual quality of output images is verified.

A popular neuron encoder model is cast into the form of an information channel, and the encoder state is shown to be measured in probability by a Markov chain. Channel capacity of the model is calculated under the assumption that the neuron threshold follows an approximately Gaussian distribution. The model is also shown to be characterized in information theory terms as a finite-state indecomposable channel subject to intersymbol interference and fading. From experiments on snail neurons which were the stimulus for the modelling efforts, the hypothesis is suggested that, to the extent the model captures the actual performance of neurons, microwave radiation could significantly alter the information processing ability of neurons.

Time-series analysis is applied to model human operator dynamics in pursuit and compensatory tracking modes. The normalized residual criterion is used as a one-step analytical tool to encompass the processes of identification, estimation, and diagnostic checking. A parameter constraining technique is introduced to develop more reliable models of human operator dynamics. The human operator is adequately modeled by a second-order dynamic system both in pursuit and compensatory tracking modes. In comparing the data sampling rates, 100 ms between samples is adequate and is shown to provide better results than a 200 ms sampling. The residual power spectrum and eigenvalue analysis show that the human operator is not a generator of periodic characteristics.