Jaan Kalda

On the KdV soliton formation and discrete spectral analysis

Abstract Based on the numerical integration (pseudospectral method) of the KdV equation governing the evolution of an initially monochromatic wave, a detailed picture of the soliton formation process is given. Systematic analysis of spectral properties of emerging KdV solitons over a wide range of dispersion parameters is presented. The number of emerging solitons is estimated from both the numerical experiment and the IST. The dynamics of spectral densities casts more light on the soliton formation process.

Non-linear analysis of the electroencephalogram for detecting effects of low-level electromagnetic fields

The study compared traditional spectral analysis and a new scale-invariant method, the analysis of the length distribution of low-variability periods (LDLVPs), to distinguish between electro-encephalogram (EEG) signals with and without a weak stressor, a low-level modulated microwave field. During the experiment, 23 healthy volunteers were exposed to a microwave (450 MHz) of 7 Hz frequency on-off modulation. The field power density at the scalp was 0.16 mW cm−2. The experimental protocol consisted of ten cycles of repetitive microwave exposure. Signals from frontal EEG channels FP1 and FP2 were analysed. Smooth power spectrum and length distribution curves of low-variability periods, as well as probability distribution close to normal, confirmed that stationarity of the EEG signal during recordings was achieved. The quantitative measure of LDLVPs provided a significant detection of the effect of the stressor for the six subjects exposed to the microwave field but for none of the sham recordings. The spectral analysis revealed a significant result for one subject only. A significant effect of the exposure to the EEG signal was detected in 25% of subjects, with microwave exposure increasing EEG variability. The effect was not detectable by power spectral measures.

Methods of electroencephalographic signal analysis for detection of small hidden changes

The aim of this study was to select and evaluate methods sensitive to reveal small hidden changes in the electroencephalographic (EEG) signal. Two original methods were considered. Multifractal method of scaling analysis of the EEG signal based on the length distribution of low variability periods (LDLVP) was developed and adopted for EEG analysis. The LDLVP method provides a simple route to detecting the multifractal characteristics of a time-series and yields somewhat better temporal resolution than the traditional multifractal analysis. The method of modulation with further integration of energy of the recorded signal was applied for EEG analysis. This method uses integration of differences in energy of the EEG segments with and without stressor. Microwave exposure was used as an external stressor to cause hidden changes in the EEG. Both methods were evaluated on the same EEG database. Database consists of resting EEG recordings of 15 subjects without and with low-level microwave exposure (450 MHz modulated at 40 Hz, power density 0.16 mW/cm2). The significant differences between recordings with and without exposure were detected by the LDLVP method for 4 subjects (26.7%) and energy integration method for 2 subjects (13.3%). The results show that small changes in time variability or energy of the EEG signals hidden in visual inspection can be detected by the LDLVP and integration of differences methods.

FRACTAL MODEL OF BLOOD VESSEL SYSTEM

A possible way of modeling of self-similar biological tree-like structures is proposed. Special attention is paid to the blood-vessel system, with elaboration on a model with certain spatial arrangement of the vessels and reasonable dependence of the blood pressure on the vessels diameter, such that the organism has a homogeneous oxygen supply. A model of the lung is also presented, which reproduces a qualitatively right dependence of the average diameter of the tubes on their generation number. The model of the blood-vessel system is based on suitably generalized Scheidegger’s model of rivers. The statistical characteristics of the modified Scheidegger’s model are established.

What does measure the scaling exponent of the correlation sum in the case of human heart rate

It is shown that in the case of human heart rate, the scaling behavior of the correlation sum (calculated by the Grassberger-Procaccia algorithm) is a result of the interplay of various factors: finite resolution of the apparatus (finite-size effects), a wide dynamic range of mean heart rate, the amplitude of short-time variability being a decreasing function of the mean heart rate. This is done via constructing a simple model of heart rhythm: a signal with functionally modulated Gaussian noise. This model reproduces the scaling behavior of the correlation sum of real medical data. The value of the scaling exponent depends on all the above-mentioned factors, and is a certain measure of short-time variability of the signal.

Turbulent mixing: the roots of intermittency

Mixing in fully developed incompressible turbulent flows is known to lead to a cascade of discontinuity fronts of passive scalar fields; these fronts make the tracer fields strongly intermittent and give rise to an anomalous scaling of structure functions. Here, a simple model, essentially a one-dimensional (1D) variant of Bakers map, is developed, which captures the main mechanism responsible for the emergence of the discontinuities. The model is studied both numerically and analytically. In particular, the structure function scaling exponent p is derived; for the Kolmogorov turbulence, p = 2 log 3 (p+1). The analytical findings are consistent with simulations, and explain the results of a series of numerical and experimental studies.

Integration of differences in EEG Analysis Reveals Changes in Human EEG Caused by Microwave

Three different methods in combination with integration of differences in signals were applied for EEG analysis to distinguish changes in EEG caused by microwave: S-parameter, power spectral density and length distribution of low variability periods. The experiments on the effect of modulated low-level microwaves on human EEG were carried out on four different groups of healthy volunteers exposed to 450 MHz microwave radiation modulated with 7 Hz, 14 Hz, 21 Hz, 40 Hz, 70 Hz, 217 or 1000 Hz frequencies. The field power density at the scalp was 0.16 mW/cm2. The EEG analysis performed for individuals with three different methods showed that statistically significant changes occur in the EEG rhythms energy and dynamics between 12% and 30% of subjects

On the topologic structure of economic complex networks: Empirical evidence from large scale payment network of Estonia

This paper presents the first topological analysis of the economic structure of an entire country based on payments data obtained from Swedbank. This data set is exclusive in its kind because around 80% of Estonias bank transactions are done through Swedbank, hence, the economic structure of the country can be reconstructed. Scale-free networks are commonly observed in a wide array of different contexts such as nature and society. In this paper, the nodes are comprised by customers of the bank (legal entities) and the links are established by payments between these nodes. We study the scaling-free and structural properties of this network. We also describe its topology, components and behaviors. We show that this network shares typical structural characteristics known in other complex networks: degree distributions follow a power law, low clustering coefficient and low average shortest path length. We identify the key nodes of the network and perform simulations of resiliency against random and targeted attacks of the nodes with two different approaches. With this, we find that by identifying and studying the links between the nodes is possible to perform vulnerability analysis of the Estonian economy with respect to economic shocks.

On the Fractality of the Biological Tree-like Structures

The fractal tree-like structures can be divided into three classes, according to the value of the similarity dimension Ds:Ds D, where D is the topological dimension of the embedding space. It is argued that most of the physiological tree-like structures have Ds≥D. The notion of the self-overlapping exponent is introduced to characterise the trees with Ds>D. A model of the human blood-vessel system is proposed. The model is consistent with the processes governing the growth of the blood-vessels and yields Ds=3.4. The model is used to analyse the transport of passive component by blood.

Analysis of surface current properties in the Gulf of Finland using data from surface drifters

The accurate prediction of currents in the ocean surface layer is of importance for many applications, such as environmental monitoring, offshore commercial operations, and safety of shipping. Numerical models can be used to obtain such predictions, but in most sea areas the availability of current observations remains scarce. We report results of field experiments involving passive surface drifters in the Gulf of Finland, with the purpose to characterize the mesoscale and sub-mesoscale flow dynamics and spreading rate. A total of 51 deployments of surface drifters were made in 2011 and 2013, with duration of drift lasting from 1 to 35 days. The individual tracks produced a velocity distribution with a mean value close to 0.1 m/s, with close resemblance to the Rayleigh distribution. A Lagrangian integral time scale was calculated based on the autocorrelation of the drifter velocity, using three different methods of calculation and splitting the drifter into segments of different duration. The persistency of motion was 7-12 hours on average, with individual trajectories showing persistent motion up to over 20 hours. When inertial oscillations were filtered out from the drifter positions, the average persistency increased to 14-20 hours. Analysis was also made for the relative dispersion of drifter clusters. At small separation scales the speed of drifter separation appears to follow the Richardsons Law, where the relative diffusivity increases as the separation distance to the 1/3 power. However, a transition takes place with separation distances close to 5 km, after which the relative diffusivity decreases with increasing separation distance. These results point to the complexity of the underlying surface current fields, and indicate what scales must be resolved in numerical models in order to obtain reliable predictions for surface currents in the Gulf of Finland.