A. N. Pavlov

Double-wavelet approach to studying the modulation properties of nonstationary multimode dynamics

On the basis of double-wavelet analysis, the paper proposes a method to study interactions in the form of frequency and amplitude modulation in nonstationary multimode data series. Special emphasis is given to the problem of quantifying the strength of modulation for a fast signal by a coexisting slower dynamics and to its physiological interpretation. Application of the approach is demonstrated for a number of model systems, including a model that generates chaotic dynamics. The approach is then applied to proximal tubular pressure data from rat nephrons in order to estimate the degree to which the myogenic dynamics of the afferent arteriole is modulated by the slower tubulo-glomerular dynamics. Our analysis reveals a significantly stronger interaction between the two mechanisms in spontaneously hypertensive rats than in normotensive rats.

Scaling features of multimode motions in coupled chaotic oscillators

Abstract Two different methods (the WTMM- and DFA-approaches) are applied to investigate the scaling properties in the return-time sequences generated by a system of two coupled chaotic oscillators. Transitions from twomode asynchronous dynamics (torus or torus–chaos) to different states of chaotic phase synchronization are found to significantly reduce the degree of multiscality. The influence of external noise on the possibility of distinguishing the various chaotic states is considered.

Multiscality in the dynamics of coupled chaotic systems

We investigate the scaling features of complex motions in systems of two coupled chaotic oscillators by means of the wavelet-transform modulus maxima method and the detrended fluctuation analysis. We show that the transition from asynchronous to synchronous dynamics typically reduces the degree of multiscality in the characteristic temporal scales. Correlation properties caused by adjustment of the involved time scales are discussed, and experimental results for coupled functional units of the kidney are analyzed.

Quantifying chaotic dynamics from integrate-and-fire processes

Characterizing chaotic dynamics from integrate-and-fire (IF) interspike intervals (ISIs) is relatively easy performed at high firing rates. When the firing rate is low, a correct estimation of Lyapunov exponents (LEs) describing dynamical features of complex oscillations reflected in the IF ISI sequences becomes more complicated. In this work we discuss peculiarities and limitations of quantifying chaotic dynamics from IF point processes. We consider main factors leading to underestimated LEs and demonstrate a way of improving numerical determining of LEs from IF ISI sequences. We show that estimations of the two largest LEs can be performed using around 400 mean periods of chaotic oscillations in the regime of phase-coherent chaos. Application to real data is discussed.

Adaptive wavelet transform-based method for recognizing characteristic oscillatory patterns

The problem concerning the automatic recognition of characteristic oscillatory patterns in multicomponent signals is investigated using the brain’s electric activity records, electroencephalograms (EEGs), as an example. It has been ascertained that recognition errors can be decreased by optimally selecting continuous wavelet transform (CWT) parameters to obtain characteristics describing the most important information on analyzed patterns. The adaptive CWT-based method for identifying the characteristic types of EEG rhythmic activity is proposed.

Estimating the predictability time of noisy chaotic dynamics from point sequences

A method for increasing the accuracy of estimation of the predictability time of noisy chaotic dynamics from system-related point sequences is proposed. General laws observed in the application of this method to interspike interval series of model threshold devices of two types operating in the regime of phase-coherent chaos are illustrated.

Speech signal filtration using double-density dual-tree complex wavelet transform

We consider the task of increasing the quality of speech signal cleaning from additive noise by means of double-density dual-tree complex wavelet transform (DDCWT) as compared to the standard method of wavelet filtration based on a multiscale analysis using discrete wavelet transform (DWT) with real basis set functions such as Daubechies wavelets. It is shown that the use of DDCWT instead of DWT provides a significant increase in the mean opinion score (MOS) rating at a high additive noise and makes it possible to reduce the number of expansion levels for the subsequent correction of wavelet coefficients.

Changes in the cerebral blood flow in newborn rats assessed by LSCI and DOCT before and after the hemorrhagic stroke

The incidence of perinatal hemorrhagic stroke (HS) is very similar to that in the elderly and produces a significant morbidity and long-term neurologic and cognitive deficits. There is strong evidence that cerebral blood flow (CBF) abnormalities make considerable contribution to HS development. However, the mechanisms responsible for pathological changes in CBF in infants with HS are not established. Therefore, quantitative assessment of CBF may significantly advance the understanding of the nature of neonatal stroke. The aim of this investigation was to determine the particularities of alterations in macro- microcirculation in the brain of newborn rats in the different stages of stress-related development of HS using three-dimensional Doppler optical coherence tomography (DOCT) and laser speckle contrast imaging (LSCI).Our results show that cerebral veins are more sensitive to harmful effect of stress compared with microcirculatory vessels. Stress-induced progressive dilation of cerebral veins with the fall of blood flow velocity precedes HS while pathological changes in microcirculatory vessels are accompanied by development of HS. The further detailed study of cerebral venous and microcirculatory circulation would be a significant advance in development of prognostic criteria for a HS risk during the first days after birthday.

Characterizing scaling properties of complex signals with missed data segments using the multifractal analysis

The scaling properties of complex processes may be highly influenced by the presence of various artifacts in experimental recordings. Their removal produces changes in the singularity spectra and the Hölder exponents as compared with the original artifacts-free data, and these changes are significantly different for positively correlated and anti-correlated signals. While signals with power-law correlations are nearly insensitive to the loss of significant parts of data, the removal of fragments of anti-correlated signals is more crucial for further data analysis. In this work, we study the ability of characterizing scaling features of chaotic and stochastic processes with distinct correlation properties using a wavelet-based multifractal analysis, and discuss differences between the effect of missed data for synchronous and asynchronous oscillatory regimes. We show that even an extreme data loss allows characterizing physiological processes such as the cerebral blood flow dynamics.

Noisy signal filtration using complex wavelet basis sets

Methods of noisy signal filtration using a discrete wavelet transform (DWT) with real basis sets of the Daubechies family are compared to methods employing a double-density dual-tree complex wavelet transform (DDCWT) with excess (nonorthonormalized) basis sets. Recommendations concerning the choice of filter parameters for minimization of the error of noisy signal filtration are formulated.