Entropy and Fractal Dimension Study of the TDP-43 Protein Low Complexity Domain Sequence in ALS Disease Severity and SARS-CoV-2 Gene Sequences in Virulence Variability

The low complexity domain (LCD) sequence has been defined in terms of entropy using a 12 amino acid sliding window along a protein sequence in the study of disease-related genes. The amyotrophic lateral sclerosis (ALS)-related TDP-43 protein sequence with intra-LCD structural information based on cryo-EM data was published recently. An application of entropy and Higuchi fractal dimension calculations was described using the Znf521 and HAR1 sequences. A computational analysis of the intra-LCD sequence entropy and Higuchi fractal dimension values at the amino acid level and at the ATCG nucleotide level were conducted without the sliding window requirement. The computational results were consistent in predicting the intermediate entropy/fractal dimension value produced when two subsequences at two different entropy/fractal dimension values were combined. The computational method without the application of a sliding-window was extended to an analysis of the recently reported virulent genes—Orf6, Nsp6, and Orf7a—in SARS-CoV-2. The relationship between the virulence functionality and entropy values was found to have correlation coefficients between 0.84 and 0.99, using a 5% uncertainty on the cell viability data. The analysis found that the most virulent Orf6 gene sequence had the lowest nucleotide entropy and the highest protein fractal dimension, in line with extreme value theory. The Orf6 codon usage bias in relation to vaccine design was discussed.

On multi-fault detection of rolling bearing through probabilistic principal component analysis denoising and Higuchi fractal dimension transformation

Bearing multi-fault detection from stochastic vibration signal is still a thorny task to dispose of because of the complex interplay between different fault components under severe noise interference. In such case, conventional techniques such as filter processing and envelope demodulation may cause undesired results. To overcome the limitation, this article explores a filtering-free technique combined probabilistic principal component analysis denoising with the Higuchi fractal dimension transformation to diagnose the bearing multi-faults. Fractal theory is used to optimize the model parameters and stabilize the random vibrational signal for fast Fourier transform spectrum analysis. Noise interference in the Higuchi transformation is capped using a probabilistic principal component analysis model whose parameters are optimized through embedding dimension Cao algorithm and correlation dimension Grassberger and Procaccia algorithm. The fault diagnostic scheme mainly falls into three steps. First, the original vibration signal is truncated into a series of sub-signal segments by moving window whose length is determined as twice the value of maximum time delay that is provided by examining the steady Higuchi fractal dimension value of a raw signal in a process of plotting the fractal dimension over a range of time delay. Then, the Higuchi approach is used to estimate the average fractal dimension for each segment to create a quasi-stationary Higuchi fractal dimension sequence on which, finally, the fault features are straightforwardly extracted by the fast Fourier transform algorithm. The effectiveness of the proposed method is validated using simulated and experimental compound bearing fault vibration signals. Some fault components may be clouded if applied Higuchi fractal dimension alone because of the noise interference, but using the probabilistic principal component analysis–Higuchi fractal dimension method leads to clear diagnostic results. It indicates that the proposed approach can be incorporated into bearing multi-fault extraction from raw vibration signals.

Investigating electroencephalography signals of autism spectrum disorder (ASD) using Higuchi Fractal Dimension

Autism spectrum disorder (ASD) is a neurodevelopmental disorder with a deficit of social relationships, interaction, sense of imagination, and constrained interests. Early diagnosis of ASD will aid in devising appropriate training procedures and placing those children in the normal stream. The objective of this research is to analyze the brain response for auditory/visual stimuli in Typically Developing (TD) and children with autism through electroencephalography (EEG). Brain dynamics in the EEG signal can be analyzed well with the help of nonlinear feature primitives. Recent research reveals that, application of fractal-based techniques proves to be effective to estimate of degree of nonlinearity in a signal. This research attempts to analyze the effect of brain dynamics with Higuchi Fractal Dimension (HFD). Also, the performance of the fractal based techniques depends on the selection of proper hyper-parameters involved in it. One of the key parameters involved in computation of HFD is the time interval parameter ‘k’. Most of the researches arbitrarily fixes the value of ‘k’ in the range of all channels. This research proposes an algorithm to estimate the optimal value of the time parameter for each channel. Sub-band analysis was also carried out for the responding channels. Statistical analysis on the experimental reveals that a difference of 30% was observed between autistic and Typically Developing children.

A Novel Multiband Spectrum Sensing Method Based on Wavelets and the Higuchi Fractal Dimension

In this work, two novel methodologies for the multiband spectrum sensing in cognitive radios are implemented. Methods are based on the continuous wavelet transform (CWT) and the multiresolution analysis (MRA) to detect the edges of available holes in the considered wideband spectrum. Besides, MRA is also combined with the Higuchi fractal dimension (a non-linear measure) to establish the decision rule permitting the detection of the absence or presence of one or multiple primary users in the studied wideband spectrum. Methods were tested on simulated and real signals showing a good performance. The results present these two methods as effective options for detecting primary user activity on the multiband spectrum. The first methodology works for 95% of cases, while the second one presents 98% of effectivity under simulated signals of signal-to-noise ratios (SNR) higher than 0 dB.