Cross-sectional view echocardiography is an efficient non-invasive diagnostic tool for characterizing Myocardial Infarction (MI) and stages of expansion leading to heart failure. An automated computer-aided technique of cross-sectional echocardiography feature assessment can aid clinicians in early and more reliable detection of MI patients before subsequent catastrophic post-MI medical conditions. Therefore, this paper proposes a novel Myocardial Infarction Index (MII) to discriminate infarcted and normal myocardium using features extracted from apical cross-sectional views of echocardiograms. The cross-sectional view of normal and MI echocardiography images are represented as textons using Maximum Responses (MR8) filter banks. Fractal Dimension (FD), Higher-Order Statistics (HOS), Hu's moments, Gabor Transform features, Fuzzy Entropy (FEnt), Energy, Local binary Pattern (LBP), Renyi's Entropy (REnt), Shannon's Entropy (ShEnt), and Kapur's Entropy (KEnt) features are extracted from textons. These features are ranked using t-test and fuzzy Max-Relevancy and Min-Redundancy (mRMR) ranking methods. Then, combinations of highly ranked features are used in the formulation and development of an integrated MII. This calculated novel MII is used to accurately and quickly detect infarcted myocardium by using one numerical value. Also, the highly ranked features are subjected to classification using different classifiers for the characterization of normal and MI LV ultrasound images using a minimum number of features. Our current technique is able to characterize MI with an average accuracy of 94.37%, sensitivity of 91.25% and specificity of 97.50% with 8 apical four chambers view features extracted from only single frame per patient making this a more reliable and accurate classification.
This work is the consideration of a fractal fractional mathematical model on the transmission and control of corona virus (COVID-19), in which the total population of an infected area is divided into susceptible, infected and recovered classes. We consider a fractal-fractional order
SIR
type model for investigation of Covid-19. To realize the transmission and control of corona virus in a much better way, first we study the stability of the corresponding deterministic model using next generation matrix along with basic reproduction number. After this, we study the qualitative analysis using "fixed point theory" approach. Next, we use fractional Adams-Bashforth approach for investigation of approximate solution to the considered model. At the end numerical simulation are been given by matlab to provide the validity of mathematical system having the arbitrary order and fractal dimension.
Malaysian Household Income Survey data provided by the Malaysian Department of Statistics is used to provide evidence
that the upper tails of the household income distribution follows a fractal based distribution known as power-law.
Inequality measures are then applied to ascertain the levels of inequality based on this distribution. In addition to that,
we analyzed the data in terms of different classes of occupation, obtained power-law exponents for each class and then
highlighted the inequality between these classes.
Stroke survivors are more prone to developing cognitive impairment and dementia. Dementia detection is a challenge for supporting personalized healthcare. This study analyzes the electroencephalogram (EEG) background activity of 5 vascular dementia (VaD) patients, 15 stroke-related patients with mild cognitive impairment (MCI), and 15 control healthy subjects during a working memory (WM) task. The objective of this study is twofold. First, it aims to enhance the discrimination of VaD, stroke-related MCI patients, and control subjects using fuzzy neighborhood preserving analysis with QR-decomposition (FNPAQR); second, it aims to extract and investigate the spectral features that characterize the post-stroke dementia patients compared to the control subjects. Nineteen channels were recorded and analyzed using the independent component analysis and wavelet analysis (ICA-WT) denoising technique. Using ANOVA, linear spectral power including relative powers (RP) and power ratio were calculated to test whether the EEG dominant frequencies were slowed down in VaD and stroke-related MCI patients. Non-linear features including permutation entropy (PerEn) and fractal dimension (FD) were used to test the degree of irregularity and complexity, which was significantly lower in patients with VaD and stroke-related MCI than that in control subjects (ANOVA; p ˂ 0.05). This study is the first to use fuzzy neighborhood preserving analysis with QR-decomposition (FNPAQR) dimensionality reduction technique with EEG background activity of dementia patients. The impairment of post-stroke patients was detected using support vector machine (SVM) and k-nearest neighbors (kNN) classifiers. A comparative study has been performed to check the effectiveness of using FNPAQR dimensionality reduction technique with the SVM and kNN classifiers. FNPAQR with SVM and kNN obtained 91.48 and 89.63% accuracy, respectively, whereas without using the FNPAQR exhibited 70 and 67.78% accuracy for SVM and kNN, respectively, in classifying VaD, stroke-related MCI, and control patients, respectively. Therefore, EEG could be a reliable index for inspecting concise markers that are sensitive to VaD and stroke-related MCI patients compared to control healthy subjects.
Studies conducted on the various geometric properties of skeletons of water bodies have shown highly promising results. However, these studies were made under the assumption that water bodies were static objects and that they remained constant over time. Water bodies are actually dynamic objects; they go through significant spatio-temporal changes due to drought and flood. In this study, the characterization of skeletons of simulated drought and flood of water bodies was performed. It was observed that as the drought level increased from 1 to 9, the average length of the skeletons decreased due to reduction in the size of the water bodies and increase in the number of water bodies. As the drought level increased from 9 to 15, the average length of the skeletons increased further due to vanishing of small water bodies. Flood caused an increase in the average length of the skeletons due to merging of adjacent water bodies. Power law relationships were observed between the average length of the skeletons of the simulated drought/flood and the level of drought/flood. The scaling exponent of these power laws which was named as a fractal dimension, indicated the rate of change of the average length of the skeletons of simulated drought/flood of water bodies over varying levels of drought/flood. However, errors observed in the goodness of fit of the plots indicated that monofractals were not sufficient to characterise the skeletons of simulated drought and flood of water bodies. Multifractals and lacunarity analysis were required for more accurate characterisation.
Analysis of human brain activity is an important topic in human neuroscience. Human brain activity can be studied by analyzing the electroencephalography (EEG) signal. In this way, scientists have employed several techniques that investigate nonlinear dynamics of EEG signals. Fractal theory as a promising technique has shown its capabilities to analyze the nonlinear dynamics of time series. Since EEG signals have fractal patterns, in this research we analyze the variations of fractal dynamics of EEG signals between four datasets that were collected from healthy subjects with open-eyes and close-eyes conditions, patients with epilepsy who did and patients who did not face seizures. The obtained results showed that EEG signal during seizure has greatest complexity and the EEG signal during the seizure-free interval has lowest complexity. In order to verify the obtained results in case of fractal analysis, we employ approximate entropy, which indicates the randomness of time series. The obtained results in case of approximate entropy certified the fractal analysis results. The obtained results in this research show the effectiveness of fractal theory to investigate the nonlinear structure of EEG signal between different conditions.
Brain activity analysis is an important research area in the field of human neuroscience. Moreover, a subcategory in this field is the classification of brain activity in terms of different brain disorders. Since the Electroencephalography (EEG) signal is, in fact, a non-linear time series, employing techniques to investigate its non-linear structure is rather crucial. In this study, we evaluate the non-linear structure of the EEG signal between healthy and schizophrenic adolescents using fractal theory. The results of our analysis revealed that in terms of all recording channels, the EEG signal of healthy subjects is more complex compared to the ones suffering from schizophrenia. The statistical analysis also indicated that there is a significant difference in the complex structure of the EEG signal between these two groups of subjects. We also utilized approximate entropy in our analysis in order to verify the obtained results of the fractal analysis. The result of the entropy analysis suggested that EEG signal for healthy subjects is less random compared to the EEG signal in schizophrenic individuals. In addition, the employed methodology in this research can be further investigated in order to classify the brain activity in terms of other brain disorders, where one can explore how the complex structure of the EEG signal alters between them.
Cardiovascular diseases (CVDs) are the leading cause of deaths worldwide. The rising mortality rate can be reduced by early detection and treatment interventions. Clinically, electrocardiogram (ECG) signal provides useful information about the cardiac abnormalities and hence employed as a diagnostic modality for the detection of various CVDs. However, subtle changes in these time series indicate a particular disease. Therefore, it may be monotonous, time-consuming and stressful to inspect these ECG beats manually. In order to overcome this limitation of manual ECG signal analysis, this paper uses a novel discrete wavelet transform (DWT) method combined with nonlinear features for automated characterization of CVDs. ECG signals of normal, and dilated cardiomyopathy (DCM), hypertrophic cardiomyopathy (HCM) and myocardial infarction (MI) are subjected to five levels of DWT. Relative wavelet of four nonlinear features such as fuzzy entropy, sample entropy, fractal dimension and signal energy are extracted from the DWT coefficients. These features are fed to sequential forward selection (SFS) technique and then ranked using ReliefF method. Our proposed methodology achieved maximum classification accuracy (acc) of 99.27%, sensitivity (sen) of 99.74%, and specificity (spec) of 98.08% with K-nearest neighbor (kNN) classifier using 15 features ranked by the ReliefF method. Our proposed methodology can be used by clinical staff to make faster and accurate diagnosis of CVDs. Thus, the chances of survival can be significantly increased by early detection and treatment of CVDs.
Myocardial infarction (MI), also referred to as heart attack, occurs when there is an interruption of blood flow to parts of the heart, due to the acute rupture of atherosclerotic plaque, which leads to damage of heart muscle. The heart muscle damage produces changes in the recorded surface electrocardiogram (ECG). The identification of MI by visual inspection of the ECG requires expert interpretation, and is difficult as the ECG signal changes associated with MI can be short in duration and low in magnitude. Hence, errors in diagnosis can lead to delay the initiation of appropriate medical treatment. To lessen the burden on doctors, an automated ECG based system can be installed in hospitals to help identify MI changes on ECG. In the proposed study, we develop a single-channel single lead ECG based MI diagnostic system validated using noisy and clean datasets. The raw ECG signals are taken from the Physikalisch-Technische Bundesanstalt database. We design a novel two-band optimal biorthogonal filter bank (FB) for analysis of the ECG signals. We present a method to design a novel class of two-band optimal biorthogonal FB in which not only the product filter but the analysis lowpass filter is also a halfband filter. The filter design problem has been composed as a constrained convex optimization problem in which the objective function is a convex combination of multiple quadratic functions and the regularity and perfect reconstruction conditions are imposed in the form linear equalities. ECG signals are decomposed into six subbands (SBs) using the newly designed wavelet FB. Following to this, discriminating features namely, fuzzy entropy (FE), signal-fractal-dimensions (SFD), and renyi entropy (RE) are computed from all the six SBs. The features are fed to the k-nearest neighbor (KNN). The proposed system yields an accuracy of 99.62% for the noisy dataset and an accuracy of 99.74% for the clean dataset, using 10-fold cross validation (CV) technique. Our MI identification system is robust and highly accurate. It can thus be installed in clinics for detecting MI.
Cable joint insulation breakdown may cause a huge loss to power companies. Therefore, it is vital to diagnose the insulation quality to detect early signs of insulation failure. It is well known that there is a correlation between Partial discharge (PD) and the insulation quality. Although many works have been done on PD pattern recognition, it is usually performed in a noise free environment. Also, works on PD pattern recognition in actual cable joint are less likely to be found in literature. Therefore, in this work, classifications of actual cable joint defect types from partial discharge data contaminated by noise were performed. Five cross-linked polyethylene (XLPE) cable joints with artificially created defects were prepared based on the defects commonly encountered on site. Three different types of input feature were extracted from the PD pattern under artificially created noisy environment. These include statistical features, fractal features and principal component analysis (PCA) features. These input features were used to train the classifiers to classify each PD defect types. Classifications were performed using three different artificial intelligence classifiers, which include Artificial Neural Networks (ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS) and Support Vector Machine (SVM). It was found that the classification accuracy decreases with higher noise level but PCA features used in SVM and ANN showed the strongest tolerance against noise contamination.