Wavelet-based multifractal analysis and fractal Signature of SARS-Cov-2 Coronavirus Variants genomes.

In this paper, the SARS-CoV-2 coronavirus variants of concern and of interest genomes are analyzed using the wavelet transform modulus maxima lines (WTMM) method. The goal is to track the monofractal behavior of the virus genomes and to investigate the Long-Range-Correlation (LRC) character through the estimation of the Hurst exponent. The obtained results demonstrate the multifractal and the anti-correlated characters in the variants of concern for the Knucleotidic and GC DNA coding. The fractal signatures of SARS-CoV-2 coronavirus variants are investigated through the indicator matrix maps of the genomes, they exhibit the same patterns for the variants (Alpha, Delta) and (Eta, Lota, Kappa) with moving positions, while the variants Beta, Gamma and Epsilon have different indicator matrixes. The fractal dimensions of SARS-CoV-2 variants are oscillating aroundI, except the Epsilon variant from USA, where the fractal dimension is 1.70.

Multifractal correlation using wavelet transform modulus maxima

The wavelet transform modulus maxima method (WTMM) for a single time series is generalized to multiple time series. The new method, which is called the joint WTMM analysis in this work, allows analyses of multifractal correlation between simultaneously measured data. Dependent, partly dependent and independent binomial cascades are used to test the joint WTMM formulism and the degree of correlation assessed qualitatively is found to agree well with the theoretical predictions. Finally, the technique is applied to simultaneously measured surface scalp potential and heart rate data taken from two healthy human subjects. Via this new method, it is shown that there is multifractal correlation between the fractal dynamics in the cortex and the autonomic regulation of the heart rate.

Multifractal correlation using wavelet transform modulus maxima

The wavelet transform modulus maxima method (WTMM) for a single time series is generalized to multiple time series. The new method, which is called the joint WTMM analysis in this work, allows analyses of multifractal correlation between simultaneously measured data. Dependent, partly dependent and independent binomial cascades are used to test the joint WTMM formulism and the degree of correlation assessed qualitatively is found to agree well with the theoretical predictions. Finally, the technique is applied to simultaneously measured surface scalp potential and heart rate data taken from two healthy human subjects. Via this new method, it is shown that there is multifractal correlation between the fractal dynamics in the cortex and the autonomic regulation of the heart rate.

Interpretation for magnetic data at low latitude areas using continuous wavelet transform and marquardt algorithm

As analyzing geomagnetic data at low latitude areas for instance the Mekong Delta (latitudes 11,07o), significant problem is that both of the magnetization and ambient field are not vertical totally, making magnetic anomalies antisymmetrical and often skewed to the location of the sources. In this paper, two-dimensional continuous wavelet transform (2-D CWT), using Farshad-Sailhac complex wavelet function is studied and applied for reducing the magnetic anomaly to a symmetrical one - this located on the source of the anomaly, and then determining the position of the center of the object causing anomalies by wavelet transform modulus maxima (WTMM) method. Next, magnetic data is extracted in two perpendicular directions passing through the center of the source to perform one-dimensional continuous wavelet transform (1-D CWT) to estimate the shape, depth and size of the source. Then, using the Marquardt algorithm to solve the inverse problem by least-squares method to further identify other characteristic parameters of the source such as: vertical size, remanent magnetization vector. The reliability of the proposed method is verified through theoretical models before application for analyzing the geomagnetic data in the Mekong Delta. The results are consistency with deep hole data, having small root mean square error, contribute to a better interpretation of the geological nature of the magnetic anomaly sources in the study area.

Multifractal analysis for seismic wave in Kathmandu valley after Gorkha Earthquake-2015, Nepal

We applied the multiscale signal processing technique, the Wavelet Transform Modulus Maxima (WTMM) to characterize high frequency properties of strong motion waveforms, in particular the temporal distribution and strength of singularities in Gorkha earthquake, 25th April 2015. We first explored their relation to earthquake data source. Then we applied the WTMM analysis to strong motion recordings. These showed that the timing and exponent of singularities measured by the WTMM method on the ground motion wave field are directly related to the position and exponent of assumed initial stress singularities on the fault plane. We found strong motion recordings at near the epicenter site have very high multifractality than far sites. Some differences and similarities among sites were successfully detected.

Dyadic wavelet analysis of bender element signals in determining shear wave velocity

Determining shear wave velocity is a critical technique in bender element tests, as it can be readily affected by near-field effects, wave reflection, and other factors. This study proposes a new method based on the dyadic wavelet transform modulus maxima. Combining the local modulus maxima of dyadic wavelet transform approximate coefficients at fine decomposition levels and an appropriate threshold value, the proposed method can automatically detect the target point. For validation, a comparative study among the dyadic wavelet transform modulus maxima, peak-to-peak, first arrival, and cross-correlation methods was carried out using 140 sets of bender element signals. The comparison results show that the proposed method not only mitigates the adverse effects of near-field, later major peaks, and noise contamination, but is also more robust in estimating shear wave velocity.

Multifractal behavior of SARS-CoV-2 COVID-19 pandemic spread, case of: Algeria, Russia, USA and Italy.

Here, the multifractal behavior of the SARS-CoV-2 COVID-19 pandemic daily and death cases is investigated through the so-called Wavelet Transform Modulus Maxima lines (WTMM) method, data available via the World Health Organization (WHO) dashboard of Algeria, Russia, USA and Italy are analyzed. The obtained results show the multifractal behavior of the COVID-19 pandemic data with different spectra of singularities. Keywords: Multifractal behavior, daily and death cases, WTMM, COVID-19 pandemic data

Multifractal Analysis of SARS-CoV-2 Coronavirus genomes using the wavelet transform

In this paper, the 1D Wavelet Transform Modulus Maxima lines (WTMM) method is used to investigate the Long-Range Correlation (LRC) and to estimate the so-called Hurst exponent of 21 isolate RNA sequence downloaded from the NCBI database of patients infected by SARS-CoV-2, Coronavirus, the Knucleotidic, Purine, Pyramidine, Ameno, Keto and GC DNA coding are used. Obtained results show the LRC character in the most sequences; except some sequences where the anti-correlated or the Classical Brownian motion character is observed, demonstrating that the SARS-Cov2 coronavirus undergoes mutation from a country to another or in the same country, they reveals also the complexity and the heterogeneous genome structure organization far from the equilibrium and the self-organization.

Automated Terminus Detection for Greenland's Peripheral Marine-Terminating Glaciers

Changes in the length of marine-terminating glaciers strongly influence the mass balance of glaciers, ice caps, and ice sheets. Currently, quantification of glacier length change through measurement of terminus position relies on time-consuming and subjective manual mapping techniques, limiting our ability to understand the dynamics controlling glacier terminus changes. I developed an automated method of mapping glacier terminus positions in satellite imagery using observations from a representative sample of Greenlands peripheral glaciers. The method is adapted from the 2D Wavelet Transform Modulus Maxima (WTMM) segmentation method, which has been used previously for image segmentation in biomedical and other applied science fields. The gradient-based method places edge detection lines along regions with the greatest gradient in intensity in the image, such as the contrast between glacier ice and water or glacier ice and sea ice. I quantified the accuracy of the automated method with reference to a validation dataset consisting of over 500 manual delineations and determined that the automated method is capable of mapping glacier termini over a wide range of image conditions (light to intermediate cloud cover, uniformly dim or bright lighting, etc.) within 1-pixel uncertainty. These time series generated automatically from Landsat images (which have a frequent repeat interval and a long record of images) are capable of resolving sub-seasonal to multiannual temporal patterns as well as regional patterns in terminus change for these glaciers. The terminus position time series generated from this automated method indicate that the marine-terminating peripheral glaciers in southeast Greenland undergo synchronous terminus retreat in 2016-17. Initial exploration of regional atmospheric and ocean conditions links this synchronous retreat to subsurface ocean warming and increased surface runoff.