• Fractal characteristic of EEG signal is not a feature of deterministic chaos
• Eu-Ba-Cu-O ceramic superconductors with critical temperature -179.4 °C

Result 1: Fractal characteristic of EEG signal is not a feature of deterministic chaos

Projects: VEGA 2/7087/27

Authors: A. Krakovská, S. Štolc., K. Šušmáková

Research in the field of chaos theory and fractals has brought new ways of looking at complex systems. In the case of many seemingly complicated real processes, it was found that the fractal dimension is low and could be modeled by small number of nonlinear differential equations with chaotic dynamics. Low fractal dimension may also be a manifestation of a special class of stochastic systems, which generate scale-invariant, fractal-like structures. While the exponential decrease in the power spectrum of high frequencies is typical for a chaotic signal, power reduction (the so-called fractal exponent) characterizes the stochastic system with 1/f noise. Our research showed that the EEG signals (representing the electrical activity of the brain) is characterized by a power decline of the spectrum with fractal exponent around 2.8. We found a strong correlation between the dimension of a fractal exponent. This shows that the low estimates of the EEG dimensions should be credited to the stochastic system with 1/f noise (Krakovská, Štolc, 2008). The presence of the scale-invariant structures in the dynamics of the human brain remains an important discovery. This is a key feature of brain activity, which confirms the success of fractal exponent to detect specific states of brain activity, eg. phase of sleep, (Šušmáková, Krakovská, 2008).

Figure: Hypnogram from the all-night EEG measurements: Expert classification of sleep stages (first image) compared with estimates of the fractal dimension of 30-seconds EEG segments (second graph). Fractal properties of EEG are becoming a promising candidate for automatic detection of the sleep stages.

Publications:

• KRAKOVSKÁ, A. - ŠTOLC, S.: Spectral decay vs. correlation dimension of EEG. Neurocomputing, 71, 2008, 13-15, 2978-2985.
• ŠUŠMÁKOVÁ, K. - KRAKOVSKÁ, A.: Discrimination ability of individual measures used in sleep stages classification. Artificial Intelligence in Medicine, 44, 2008, 261-277.

Result 2: Eu-Ba-Cu-O ceramic superconductors with critical temperature -179 °C

Projects: VEGA 2/7083/27

Authors: A. Cigáň, J. Maňka, J. Polovková, M. Kopčok, P. Jurdák, K. Jurča

 In the Institute of Measurement Science, bulk high-temperature superconductor based on Eu-Ba-Cu-O was prepared. Its synthesis conditions were optimalized and effects of stoichiometric deviations of Eu and Ba cations from parent Eu₁Ba₂Cu₃O_y composition were studied. Two series of samples, Eu_1+xBa_2-xCu₃O_y and Eu_1-xBa_2+xCu₃O_y, with excess Eu and Ba content (x), respectively, were synthesized in flowing oxygen, where x ranges from 0 to 0.1. In the studied interval of composition deviation values of the critical temperatures, T_c(R=0), maximum of volume magnetization, M_max, and volume density were higher than 91 K, 10⁴ Am^-1 and 6.4 g cm^-3, respectively. In the first series increasing excess Eu content results in the improvement of inter-grain properties, T_c, of the first magnetic penetration field, H_p1, and M_max achieving maximum at excess Ba levels x = 0.02- 0.04. Following increasing of Ba level, x ≥ 0.05, results in a significant decrease of M_max. On contrary, in the second series, the volume magnetization is almost unvaried with increasing excess barium. The obtained results can be used e.g., in engineering of high temperature superconductors for high current applications. Looking for the superconductors, the materials with resistance-less conduction of high electric current is motivated by a decrease of the transport energy losses and effort to produce superconducting magnets with ultra high magnetic field or levitation transport systems.

Publications:

• CIGÁŇ, Alexander - MAŇKA, Ján - KOPČOK, Michal - POLOVKOVÁ, Júlia - JURDÁK, Peter - KOŇAKOVSKÝ, Anton. Effects of europium-barium nonstoichiometry in EBCO123 systems on transition and magnetization properties. In Acta Physica Polonica A. ISSN 0587-4246, 2008, vol. 113, no. 1, p. 219-222. (0.340 - IF2007).
• CIGÁŇ, Alexander - MAŇKA, Ján - POLOVKOVÁ, Júlia - MAJEROVÁ, Melinda - KOPČOK, Michal - VAN DRIESSCHE, I. - ZRUBEC, Vladimír. Study of light nonstoichiometry in Eu-Ba-Cu-O systems. In Journal of Physics: Conference Series. ISSN 1742-6588, 2008, vol. 97, art. no. 012184. (Scopus)