“…We used three different nonlinear techniques: Lyapunov exponent, detrended fluctuation analysis and fractal dimension to assess the underlying behavior of mood and energy fluctuations in all groups; and subsequently to assess whether these arise from different processes in each of these groups. …”
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“…Topics covered include interactions between biological molecules, physical chemistry of phospholipids association into bilayer membranes, DNA and protein structure and folding, passive and active electrical properties of the cell membrane, classical as well as fractal aspects of reaction kinetics and diffusion in biological systems, structural and functional aspects of molecular machines (including channels, ion pumps, and light-harvesting antenna), as well as fundamental aspects of proteins association in solutions and in living cells.…”
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“…Much of the content is informed by its applicability: Fourier analysis is developed to the point where it can be rigorously applied to partial differential equations or computation, and the theory of metric spaces includes applications to ordinary differential equations and fractals. Essential Real Analysis will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis. …”
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“…Since both the multifractal Schrödinger equation from the Scale Relativity Theory and the General Relativity equations for a gravitational field with axial symmetry accept the same SL(2R)-type invariance, an Ernst-type potential (from General Relativity) and also a multi-fractal tensor (from Scale Relativity) are highlighted in the description of complex systems dynamics. …”
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“…The corresponding escape basins have a fractal nature that can be revealed by the so-called basin entropy, a novel concept developed to quantify final-state uncertainty in dynamical systems. …”
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“…We have included studies that used the three most common non-linear indices: power law slope, the short term fractal scaling exponent and measures based on Poincare plots. …”
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“…We suppose that the timekeeper represents a fractal source in the system, and that a process of estimation of the half-period of the metronome, obeying a random-walk dynamics, combines with the linear phase correction process. …”
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“…The bulk property was however considered as Intensity Level based Multi-fractal Dimension (ILMFD) of ordinary microscopic images of heat denatured protein aggregates which was known to have potential to serve as protein marker. …”
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“…Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely although they can be predicted to some extent in line with the chaos theory Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory, A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms.…”
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“…A fractal signal x(t) in biomedical engineering may be characterized by 1/f noise, that is, the power spectrum density (PSD) divergences at f = 0. …”
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“…Texture quantification techniques include structural-, model- (fractal dimensions), statistical- and frequency-based methods. …”
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“…The yield stress of these membranes, measured for the first time via the fractal dimension, is intimately related to the degree of polymerisation probably through a 2D disorder that quenches the lateral diffusion of the lipid molecules. …”
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“…Self-similarity and thus randomness of size-number distribution prevailed after tillage regardless of the intensity of disturbance imposed by cultivation. The values of fractal dimensions before and after tillage were low, suggesting that short-term, short-range factors govern size-number distribution of soil seed banks.…”
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“…Pores in single crystalline semiconductors come in many forms (e.g., pore sizes from 2 nm to > 10 µm; morphologies from perfect pore crystal to fractal) and exhibit many unique properties directly or as nanocompounds if the pores are filled. …”
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“…Here we further analyze these structures and provide the first evidence that G1 phase chromosomes are knotted, consistent with the fact that plots of contact probability vs sequence separation show a power law dependence that is intermediate between that of a fractal globule and an equilibrium structure.…”
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“…The article reviews the fascial structure that involves and forms the diaphragm muscle with the aim of changing the vision of this complex muscle: from an anatomical and mechanistic form to a fractal and asynchronous form. Another step forward for understanding the diaphragm muscle is that it is not only covered, penetrated and made up of connective tissue, but the contractile tissue itself is a fascial tissue with the same embryological derivation. …”
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“…Specifically we propose a novel approach for administrative logo detection based on a fuzzy classification with a multi-fractal texture feature, capable of automatically characterizing texture measures describing logo and non-logo regions. …”
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“…The subdiffusion that emerges in such a high-dimensional, fractal environment leads to a Fokker–Planck Equation with a fractional time derivative. …”
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“…However, some other properties of these allotropic modifications of carbon, e.g., fractal properties, are poorly understood. In this work, the spatial series (interatomic distance histograms) calculated using the crystal structures of diamond and graphite are investigated. …”
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