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Ionescu Ana-Maria, Dumitrescu Cătălin, Copaci Carmen, Iliescu Dan, Hangan Tony and Bobe Alexandru

Abstract

Electroencephalogram (EEG) analysis consists of locating signal structtures in time and frequency. A detection method based on the Matching Pursuit Algorithms finds the suboptimal solution of the function optimal linear expansion over a redundant waveform dictionary. This paper has put forth a method for the automatic detection and analysis of transient waves during sleep based on the matching pursuit method with a real dictionary og Gabor functions. Each wave peak is described in terms of natural parameters. In this context, there have been confirmed several literature hypotheses regarding the spatial, temporal, and frequency distribution of transient waves during sleep, and their relationships with slow wave brain activity. Mastery and expertise in clinical EEG interpretation is one of the most desirable disgnostic clinical skills in interpreting seizures, epilepsy, sleep disorder, biomarkers for early disgnosis of Parkinson’s and Alzheimer’s disease, and other neurocognitive studies.

Open access

Dumitrescu Cătălin, Copaci Carmen, Iliescu Dan, Hangan Tony, Ionescu Ana-Maria and Bobe Alexandru

Abstract

The wide variety of waveform in EEG signals and the high non-stationary nature of many of them is one of the main difficulties to develop automatic detection system for them. In sleep stage classification a relevant transient wave is the K-complex. This paper comprehend the developing of two algorithms in order to achieve an automatic K-complex detection from EEG raw data. These algorithms are based on a time-frequency analysis and two time-frequency techniques, the Short Time Fourier Transform (STFT) and the Continuous Wavelet Transform (CWT), are tested in order to find out which one is the best for our purpose, being of two wavelet functions to measure the capability of them to detect K-complex and to choose one to be employed in the algorithms. The first algorithm is based on the energy distribution of the CWT detecting the spectral component of the K-complex. The second algorithm is focused on the morphology of the K-complex / sleep spindle waveform after the CWT. Evaluating the algorithms results reveals that a false K-complex detection is as important as real K-complex detection.

Open access

Alexandru Bobe, Aurelian Nicola and Constantin Popa

Abstract

In an earlier paper [J. of Appl. Math. and Informatics, 29(3-4)(2011), 697-712] we proposed a general projection-type algorithm with corrections and proved its convergence under a set of special assumptions. In this paper we prove convergence of this algorithm under a much weaker set of assumptions. This new framework gives us the possibility to obtain as a particular case of our method the two-step algorithm analysed in [B I T, 38(2)(1998), 275-282].

Open access

Alexandru Bobe, Wladimir G. Boskoff and Marian G. Ciucă

Abstract

In this article we introduce three centro-affine invariant functions in Minkowski spaces. Tzitzeica curves and Tzitzeica surfaces may be defined in this new context. Our main results allow us to understand the connections between Tzitzeica curves and surfaces in Minkowski spaces and the original Tzitzeica curves and surfaces from the Euclidian space

Open access

Wladimir G. Boskoff, Şerban Bărcănescu and Alexandru Bobe

Abstract

Working in the context of Hilbert's axiomatic system, we prove that the Tzitzeica-Johnson configuration has sense in neutral geometry. The elements of a Tzitzeica-Johnson configuration allow us to analyse the Euclidean or the non-Euclidean character of the metric of the plane