“…However, we have found a signature that SARS-CoV-2 proteins were evolving at a higher rate, and considering global data, mutations are detected in the majority of the available amino acid locations. Fractal analysis of each protein's normalized factor time series showed a periodically aperiodic emergence of dominant variants for SARS-CoV-2 protein mutations across different countries. …”
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“…The self-compiled RF time series signal analysis software was used to extract 3 different dimensions of parameters of the region of interest (ROI), including time domain, frequency domain, and fractal dimension (FD). Fourteen spectrum characteristic parameters were extracted, of which structure function method FD (SFD) and Higuchi FD belonged to FD parameters; slope, intercept, midbandfit, S1, S2, S3, and S4 were frequency domain parameters; and fuzzy entropy, kurtosis, peak, cross zero count, and cross zero standard deviation (Std) were time domain parameters. …”
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“…With the mixed linear model (MLM) in the Tassel software, we identified 834 SNPs associated with root surface area (RSA), root length (RL), root branch number (RBN), root number (RN), plant dry weight (PDW), plant height (PH), root volume (RL), plant fresh weight (PFW), root fractal dimension (RFD), number of root nodes (NRN), and average root diameter (ARD), with a significant level of p < 2.39×10(–7). …”
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“…Heart rate fragmentation using the percentage of inflection points (PIP) and alpha 1-index (using fractal evaluation of NN intervals) were then calculated. …”
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“…METHODS: We used population-based observational cross-sectional data from the Maastricht Study of N=3471 participants (mean age 59.4 years, 48.4% men, 14.7% with prediabetes, 21.0% with type 2 diabetes) to study the associations, after adjustment for demographic, cardiovascular risk and lifestyle factors, between glucose metabolism status (prediabetes and type 2 diabetes vs normal glucose metabolism) plus measures of glycaemia (fasting plasma glucose, 2 h post-load glucose, HbA(1c), skin autofluorescence [SAF] and duration of diabetes) and composite Z-scores of corneal nerve fibre measures or individual corneal nerve fibre measures (corneal nerve bifurcation density, corneal nerve density, corneal nerve length and fractal dimension). We used linear regression analysis, and, for glucose metabolism status, performed a linear trend analysis. …”
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“…This type of increasing behaviour of anomalous dimension with q suggests the multi-fractal nature of emission spectra and indicates the production of particle via cascading mechanism in the high multiplicity pp events. …”
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“…Chapters 9–13 focus on discrete systems, chaos and fractals. Conjugacy relationship among maps and its properties are described with proofs. …”
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“…Percolation theory deals with clustering, criticallity, diffusion, fractals, phase transitions and disordered systems. …”
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“…What do colloids, fractals, liquid crystals, and polymers have in common? …”
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“…Penrose, a cat with a knack for math, takes children on an adventurous tour of mathematical concepts from fractals to infinity.…”
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“…Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. …”
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“…Partly motivated by this work, analysis and diffusion processes on fractals have been developed since the late eighties. …”
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“…Reversible transformations between fractals and periodic structures are of fundamental importance for understanding the formation mechanism of fractals. …”
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“…This book surveys the recent theory of wavelet transforms and its applications in various fields both within mathematics (singular integrals, localization of singularities) and beyond it, in computer vision, the physics of fractals, time-frequency analysis.…”
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“…We review here our recent work concerned with understanding of enhancement mechanisms and formation of three such substrates: silver fractals, silver coated gold nanoparticles deposited on glass and fluorescence enhancing gold colloids.…”
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“…Tippings from and into several coexisting attractors are possible, and one can find fractality-induced tipping, the consequence of the fractality of the scenario-dependent basins of attractions, as well as tipping into a chaotic attractor. …”
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“…These improvements adopt different geometric fractals, such as the Sierpinski triangle, to divide the monitoring area into multiple clusters. …”
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“…The model used the order degree of the thin films as a fractality measure of the physical system’s representation in the multifractal space. …”
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