Fractals in Neuroimaging.

Several natural phenomena can be described by studying their statistical scaling patterns, hence leading to simple geometrical interpretation. In this regard, fractal geometry is a powerful tool to describe the irregular or fragmented shape of natural features, using spatial or time-domain statistical scaling laws (power-law behavior) to characterize real-world physical systems. This chapter presents some works on the usefulness of fractal features, mainly the fractal dimension and the related Hurst exponent, in the characterization and identification of pathologies and radiological features in neuroimaging, mainly, magnetic resonance imaging.

The effect of COVID-19 pandemic on return-volume and return-volatility relationships in cryptocurrency markets.

Understanding the dynamics of cryptocurrency markets during financial crises such as the recent one caused by the COVID-19 pandemic is crucial for policy makers and investors. In this study, the effect of COVID-19 pandemic on the return-volatility and return-volume relationships for the ten most traded cryptocurrencies, namely Tether, Bitcoin, Ethereum, Ripple, Litecoin, Bitcoin Cash, EOS, Chainlink, Cardano, and Monero is examined. Further, the behavior of cryptocurrencies during COVID-19 pandemic is compared with less volatile markets such as Gold, WTI, and BRENT crude oil markets.

Nonlinear Statistical Analysis of Normal and Pathological Infant Cry Signals in Cepstrum Domain by Multifractal Wavelet Leaders.

Multifractal behavior in the cepstrum representation of healthy and unhealthy infant cry signals is examined by means of wavelet leaders and compared using the Student -test. The empirical results show that both expiration and inspiration signals exhibit clear evidence of multifractal properties under healthy and unhealthy conditions. In addition, expiration and inspiration signals exhibit more complexity under healthy conditions than under unhealthy conditions.

The effect of COVID-19 on long memory in returns and volatility of cryptocurrency and stock markets.

We examine long memory (self-similarity) in digital currencies and international stock exchanges prior and during COVID-19 pandemic. Specifically, ARFIMA and FIGARCH models are respectively employed to evaluate long memory parameter in returns and volatility. The dataset contains 45 cryptocurrency markets and 16 international equity markets.

Randomness, Informational Entropy, and Volatility Interdependencies among the Major World Markets: The Role of the COVID-19 Pandemic.

The main purpose of our paper is to evaluate the impact of the COVID-19 pandemic on randomness in volatility series of world major markets and to examine its effect on their interconnections. The data set includes equity (Bitcoin and Standard and Poor's 500), precious metals (Gold and Silver), and energy markets (West Texas Instruments, Brent, and Gas). The generalized autoregressive conditional heteroskedasticity model is applied to the return series.

Renyi entropy and mutual information measurement of market expectations and investor fear during the COVID-19 pandemic.

The COVID-19 pandemic has seriously affected world economies. In this regard, it is expected that information level and sharing between equity, digital currency, and energy markets has been altered due to the pandemic outbreak. Specifically, the resulting twisted risk among markets is presumed to rise during the abnormal state of world economy.

The impact of COVID-19 pandemic upon stability and sequential irregularity of equity and cryptocurrency markets.

We explore the evolution of the informational efficiency in 45 cryptocurrency markets and 16 international stock markets before and during COVID-19 pandemic. The measures of Largest Lyapunov Exponent (LLE) based on the Rosenstein's method and Approximate Entropy (ApEn), which are robust to small samples, are applied to price time series in order to estimate degrees of stability and irregularity in cryptocurrency and international stock markets. The amount of regularity infers on the unpredictability of fluctuations.

The Informational Dynamics of Mean‒Variance Relationships in Fertilizer Markets: An Entropic Investigation.

The risk‒return trade-off is a fundamental relationship that has received a large amount of attention in financial and economic analysis. Indeed, it has important implications for understanding linear dynamics in price returns and active quantitative portfolio optimization. The main contributions of this work include, firstly, examining such a relationship in five major fertilizer markets through different time periods: a period of low variability in returns and a period of high variability such as that during which the recent global financial crisis occurred.

Performance of machine learning methods in diagnosing Parkinson's disease based on dysphonia measures.

Parkinson's disease (PD) is a widespread degenerative syndrome that affects the nervous system. Its early appearing symptoms include tremor, rigidity, and vocal impairment (dysphonia). Consequently, speech indicators are important in the identification of PD based on dysphonic signs.

Denoising techniques in adaptive multi-resolution domains with applications to biomedical images.

Variational mode decomposition (VMD) is a new adaptive multi-resolution technique suitable for signal denoising purpose. The main focus of this work has been to study the feasibility of several image denoising techniques in empirical mode decomposition (EMD) and VMD domains. A comparative study is made using 11 techniques widely used in the literature, including Wiener filter, first-order local statistics, fourth partial differential equation, nonlinear complex diffusion process, linear complex diffusion process (LCDP), probabilistic non-local means, non-local Euclidean medians, non-local means, non-local patch regression, discrete wavelet transform and wavelet packet transform.

High-frequency-based features for low and high retina haemorrhage classification.

Haemorrhages (HAs) presence in fundus images is one of the most important indicators of diabetic retinopathy that causes blindness. In this regard, accurate grading of HAs in fundus images is crucial for appropriate medical treatment. The purpose of this Letter is to assess the relative performance of statistical features obtained with three different multi-resolution analysis (MRA) techniques and fed to support vector machine in grading retinal HAs.

Image denoising in bidimensional empirical mode decomposition domain: the role of Student's probability distribution function.

Hybridisation of the bi-dimensional empirical mode decomposition (BEMD) with denoising techniques has been proposed in the literature as an effective approach for image denoising. In this Letter, the Student's probability density function is introduced in the computation of the mean envelope of the data during the BEMD sifting process to make it robust to values that are far from the mean. The resulting BEMD is denoted tBEMD.

Automated pathologies detection in retina digital images based on complex continuous wavelet transform phase angles.

An automated diagnosis system that uses complex continuous wavelet transform (CWT) to process retina digital images and support vector machines (SVMs) for classification purposes is presented. In particular, each retina image is transformed into two one-dimensional signals by concatenating image rows and columns separately. The mathematical norm of phase angles found in each one-dimensional signal at each level of CWT decomposition are relied on to characterise the texture of normal images against abnormal images affected by exudates, drusen and microaneurysms.

Computational analyses of arteriovenous malformations in neuroimaging.

Computational models have been investigated for the analysis of the physiopathology and morphology of arteriovenous malformation (AVM) in recent years. Special emphasis has been given to image fusion in multimodal imaging and 3-dimensional rendering of the AVM, with the aim to improve the visualization of the lesion (for diagnostic purposes) and the selection of the nidus (for therapeutic aims, like the selection of the region of interest for the gamma knife radiosurgery plan). Searching for new diagnostic and prognostic neuroimaging biomarkers, fractal-based computational models have been proposed for describing and quantifying the angioarchitecture of the nidus.

Comparative study of ECG signal denoising by wavelet thresholding in empirical and variational mode decomposition domains.

Hybrid denoising models based on combining empirical mode decomposition (EMD) and discrete wavelet transform (DWT) were found to be effective in removing additive Gaussian noise from electrocardiogram (ECG) signals. Recently, variational mode decomposition (VMD) has been proposed as a multiresolution technique that overcomes some of the limits of the EMD. Two ECG denoising approaches are compared.

Automated detection of circinate exudates in retina digital images using empirical mode decomposition and the entropy and uniformity of the intrinsic mode functions.

This work presents a new automated system to detect circinate exudates in retina digital images. It operates as follows: the true color image is converted to gray levels, and contrast-limited adaptive histogram equalization (CLAHE) is applied to it before undergoing empirical mode decomposition (EMD) as intrinsic mode functions (IMFs). The entropies and uniformities of the first two IMFs are then computed to form a feature vector that is fed to a support vector machine (SVM) for classification.

New approach for automatic classification of Alzheimer's disease, mild cognitive impairment and healthy brain magnetic resonance images.

Explored is the utility of modelling brain magnetic resonance images as a fractal object for the classification of healthy brain images against those with Alzheimer's disease (AD) or mild cognitive impairment (MCI). More precisely, fractal multi-scale analysis is used to build feature vectors from the derived Hurst's exponents. These are then classified by support vector machines (SVMs).

Automatic brain MR images diagnosis based on edge fractal dimension and spectral energy signature.

A new automatic system to detect pathologies in human brain magnetic resonance (MR) images is presented. The goal is to classify normal versus abnormal images affected by Alzheimer, Glioma, Herpes, Metastatic, and Multiple Sclerosis. The extracted features are the fractal dimension of edges in the Hilbert domain, and the skewness and kurtosis of their spectral energy distribution.

Hybrid Discrete Wavelet Transform and Gabor Filter Banks Processing for Features Extraction from Biomedical Images.

A new methodology for automatic feature extraction from biomedical images and subsequent classification is presented. The approach exploits the spatial orientation of high-frequency textural features of the processed image as determined by a two-step process. First, the two-dimensional discrete wavelet transform (DWT) is applied to obtain the HH high-frequency subband image.

Alzheimer's disease detection in brain magnetic resonance images using multiscale fractal analysis.

We present a new automated system for the detection of brain magnetic resonance images (MRI) affected by Alzheimer's disease (AD). The MRI is analyzed by means of multiscale analysis (MSA) to obtain its fractals at six different scales. The extracted fractals are used as features to differentiate healthy brain MRI from those of AD by a support vector machine (SVM) classifier.

Hybrid cosine and Radon transform-based processing for digital mammogram feature extraction and classification with SVM.

A new methodology to automatically extract features from mammograms and classify them is presented. It relies on a hybrid processing system that sequentially uses the discrete cosine transform (DCT) to obtain the high frequency component of the mammogram and then applies the Radon transform to the obtained DCT image in order to extract its directional features. The features are subsequently fed to a support vector machine for classification.