In this paper, we study performance of Katz method of computing fractal dimension of waveforms, and its estimation accuracy is compared with Higuchi's method. The study is performed on four synthetic parametric fractal waveforms for which true fractal dimensions can be calculated, and real sleep electroencephalogram. The dependence of Katz's fractal dimension on amplitude, frequency and sampling frequency of waveforms is noted. Even though the Higuchi's method has given more accurate estimation of fractal dimensions, the study suggests that the results of Katz's based fractal dimension analysis of biomedical waveforms have to be carefully interpreted.
"The value of this index is usually a non-integer, fractional number; hence, the designation of a fractal dimension. There are many notions of FD, and various algorithms have been proposed to compute them (Raghavendra and Dutt, 2009). None of these methods, however, should be considered as universal, which justifies an empirical comparison of their abilities as feature extractors from EMG signals. "
[Show abstract][Hide abstract] ABSTRACT: Abstract The study of electromyographic (EMG) signals has gained increased attention in the last decades since the proper analysis and processing of these signals can be instrumental for the diagnosis of neuromuscular diseases and the adaptive control of prosthetic devices. As a consequence, various pattern recognition approaches, consisting of different modules for feature extraction and classification of EMG signals, have been proposed. In this paper, we conduct a systematic empirical study on the use of Fractal Dimension (FD) estimation methods as feature extractors from EMG signals. The usage of FD as feature extraction mechanism is justified by the fact that EMG signals usually show traces of self-similarity and by the ability of FD to characterize and measure the complexity inherent to different types of muscle contraction. In total, eight different methods for calculating the FD of an EMG waveform are considered here, and their performance as feature extractors is comparatively assessed taking into account nine well-known classifiers of different types and complexities. Results of experiments conducted on a dataset involving seven distinct types of limb motions are reported whereby we could observe that the normalized version of the Katz׳s estimation method and the Hurst exponent significantly outperform the others according to a class separability measure and five well-known accuracy measures calculated over the induced classifiers.
"In addition to the standard box-counting, circle-counting, or yardstick methods, more effective methods were developed, such as the methods by Katz , Higuchi , Sevcik , and Raghavendra and Dutt (multiresolution box-counting MRBC and multiresolution length-based MRL methods ). The choice of mathematical methods gained fresh momentum when Raghavendra and Dutt [9, 10] compared existing methods and found Katz' method  to be highly inaccurate. They also demonstrated the bad correlation of a hypnogram with the corresponding sleep EEG's fractal dimensions calculated with Katz' method, whereas Higuchi's method provided a good correlation . "
[Show abstract][Hide abstract] ABSTRACT: Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal's time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.
Computational and Mathematical Methods in Medicine 09/2013; 2013:178476. DOI:10.1155/2013/178476 · 0.77 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In this study, the in vitro antimicrobial and antiviral activities of the lysozyme from marine strain S-12-86 (LS) were investigated. The antimicrobial activity of LS was tested by minimum inhibition concentration (MIC) and minimum bactericidal concentration (MBC) method. The inhibiting effects of LS on pseudo rabies virus (PRV) in swine kidney cells (PK-15 cells) were judged by cytopathogenic effect test (CPE). The results showed LS had a broad antimicrobial spectrum against several standard strains including gram-positive bacteria, gram-negative bacteria, fungi, etc. The MIC of LS was 0.25–4.00 mg mL−1 and its MBC was 0.25–8.00 mg mL−1, respectively. Observation under the transmission electron microscope revealed that the cell wall of Candida albicans was distorted seriously, and the cytoplasm with many cavities was asymmetrical after being hydrolyzed by LS. The median cytotoxicity concentration (TC50) of LS was 100.0 μg mL−1, the median effective concentration (EC50) was 0.46 μg mL−1, and the selectivity index (TI = TC50/EC50) was 217. LS could inhibit PRV in PK-15 cells when it was added to cell culture medium at 0, 2, 4, 6, and 8 h after PK-15 cells had been infected by PRV. From the results, we concluded that LS had broad antimicrobial spectrum and good inhibiting effects on PRV.
Agricultural Sciences in China 01/2008; DOI:10.1016/S1671-2927(08)60029-2 · 0.82 Impact Factor
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