Phase Space Analysis of Cardiac Spectra

Cardiac diseases are one of the main reasons of mortality in modern, industrialized societies, and they cause high expenses in public health systems. Therefore, it is important to develop analytical methods to improve cardiac diagnostics. Electric activity of heart was first modeled by using a set of nonlinear differential equations. Latter, variations of cardiac spectra originated from deterministic dynamics are investigated. Analyzing the power spectra of a normal human heart presents His-Purkinje network, possessing a fractal like structure. Phase space trajectories are extracted from the time series graph of ECG. Lower values of fractal dimension, D indicate dynamics that are more coherent. If D has non-integer values greater than two when the system becomes chaotic or strange attractor. Recently, the development of a fast and robust method, which can be applied to multichannel physiologic signals, was reported. This manuscript investigates two different ECG systems produced from normal and abnormal human hearts to introduce an auxiliary phase space method in conjunction with ECG signals for diagnoses of heart diseases. Here, the data for each person includes two signals based on V_4 and modified lead III (MLIII) respectively. Fractal analysis method is employed on the trajectories constructed in phase space, from which the fractal dimension D is obtained using the box counting method. It is observed that, MLIII signals have larger D values than the first signals (V_4), predicting more randomness yet more information. The lowest value of D (1.708) indicates the perfect oscillation of the normal heart and the highest value of D (1.863) presents the randomness of the abnormal heart. Our significant finding is that the phase space picture presents the distribution of the peak heights from the ECG spectra, giving valuable information about heart activities in conjunction with ECG.

Understanding of Normal and Abnormal Hearts by Phase Space Analysis and Convolutional Neural Networks

Cardiac diseases are one of the leading mortality factors in modern, industrialized societies, which cause high expenses in public health systems. Due to high costs, developing analytical methods to improve cardiac diagnostics is essential. The heart's electric activity was first modeled using a set of nonlinear differential equations. Following this, variations of cardiac spectra originating from deterministic dynamics are investigated. Analyzing a normal human heart's power spectra offers His-Purkinje network, which possesses a fractal-like structure. Phase space trajectories are extracted from the time series electrocardiogram (ECG) graph with third-order derivate Taylor Series. Here in this study, phase space analysis and Convolutional Neural Networks (CNNs) method are applied to 44 records via the MIT-BIH database recorded with MLII. In order to increase accuracy, a straight line is drawn between the highest Q-R distance in the phase space images of the records. Binary CNN classification is used to determine healthy or unhealthy hearts. With a 90.90% accuracy rate, this model could classify records according to their heart status.

Mathematical and Linguistic Characterization of Orhan Pamuk's Nobel Works

In this study, Nobel Laureate Orhan Pamuk's works are chosen as examples of Turkish literature. By counting the number of letters and words in his texts, we find it possible to study his works statistically. It has been known that there is a geometrical order in text structures. Here the method based on the basic assumption of fractal geometry is introduced for calculating the fractal dimensions of Pamuk's texts. The results are compared with the applications of Zipf's law, which is successfully applied for letters and words, where two concepts, namely Zipf's dimension and Zipf's order, are introduced. The Zipf dimension of the novel My Name is Red is found to be much different than his other novels. However, it is linguistically observed that there is no fundamental difference between his corpora. The results are interpreted in terms of fractal dimensions and the Turkish language.