“…Our analysis of confocal images of biofilms formed by NTHI strain 86-028NP using pair correlations of local bacterial densities within sequential planes parallel to the substrate showed the presence of fractal structures of short length scales (≤10 μm). …”
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“…Linear (absolute and relative power of θ (4–8Hz), α 1 (8–10 Hz), α 2 (10–12 Hz), β 1 (12–16 Hz), β 2 (16–20 Hz), β 3 (20–30 Hz), γ 1 (30–40 Hz), γ 2 (40–50 Hz) and non-linear features (approximate entropy, Katz fractal dimension, Petrosian fractal dimension, spectral entropy, and sample entropy) from Fps channel were calculated. …”
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“…The probability density function tail of thermal energy dissipation gradually rises and approaches the stretched exponent function with temporal evolution. The slope of fractal dimension increases at an early time, however, the fractal dimension for the fluid interfaces is 2.4 at times t/τ ≥ 2, which demonstrates the self-similarity of the turbulent RT mixing zone in 3D space. …”
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“…First, LDH activity was measured in vitro in the presence of filamentous (F-)actin and NPs (50 and 100 nm diameter) to determine changes in viscosity and the fractal kinetics of LDH. The fractal dimension (fD) was also determined using the rescaled range analysis procedure. …”
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“…However, the generated pattern had a specific characteristic length, and the model was unable to produce a fractal structure with the model. In the present study, we focused on the anterior part of the sagittal suture and formulated a new mathematical model with time–space-dependent noise that was able to generate the fractal structure. …”
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“…"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. …”
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“…The background of a coding or noncoding DNA sequence, however, is fairly random, and can be characterized as a random fractal. When a gene-finding algorithm incorporates multiple sources of information about coding regions, it becomes more successful. …”
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“…A potential approach is to use the radiomics and fractal texture features extracted from brain tumors to characterize morphological and physiological properties. …”
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“…MAP and the long-term fractal exponent were associated with success of up-titration. …”
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“…In addition, the correlation between fractal dimension and rock composition is studied with pore-throat morphology being comprehensively analyzed. …”
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“…The aim of this study was to compare radiomorphometric indices and fractal dimension on panoramic images of patients with asthma using ICSs and healthy controls. …”
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“…The results indicate the following: (1) When 42.02s(-1) ≤[Image: see text] ≤ 49.20s(-1), the degree of fragmentation and the fractal dimension of saturated state marble is greater than that of the dry state marble; when [Image: see text] <42.02s(-1) or [Image: see text] >49.20s-(1), the dry state marble exhibits greater fragmentation than the saturated marble; (2) When the saturated state marble is subjected to a specific fractal dimension, the energy-absorbing density of the marble that characterizes the saturated state is great compared with the dry state, and when the fractal dimension increases, the energy-absorbing densities that characterize the two states gradually converge. (3) The effect of water on the mechanical properties of marble has an obvious rate dependence, showing a weakening effect at low strain rates and a strengthening effect at high strain rates. …”
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“…MEG recordings from 36 AD patients and 26 controls were analyzed by means of six entropy and complexity measures: Shannon spectral entropy (SSE), approximate entropy (ApEn), sample entropy (SampEn), Higuchi’s fractal dimension (HFD), Maragos and Sun’s fractal dimension (MSFD), and Lempel-Ziv complexity (LZC). …”
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“…Long noncoding RNA (lncRNA) within mRNA sequences of Alzheimer's disease genes, namely, APP, APOE, PSEN1, and PSEN2, has been analyzed using fractal dimension (FD) computation and correlation analysis. …”
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“…The topology of the networks involves emergence of modules and sub-modules at different levels of constitution governed by fractal laws that are signatures of self-organization in complex networks. …”
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“…In healthy individuals, the HRV signal is mainly composed of quasi‐periodic oscillations, but it also possesses random fluctuations and so‐called fractal structures. One widely applied approach to investigate fractal correlation properties of heart rate (HR) time series is the detrended fluctuation analysis (DFA). …”
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“…Combining previous publications, two areas are non-stochastic and exhibit, simultaneously, fractal, long-memory and self-organisation patterns through a combination of 15 different fractal and SOC analysis techniques. …”
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“…This new model comprises three modules: high heterogeneity of the reservoir based on the fractal system, the permeability modulus typically showing the pressure sensitivity of hydraulic fractures, and the anomalous diffusion describing non-Darcy flow turbulence. …”
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“…Synchrotron-SAXS results performed in the semidilute regimes show a fractal chain conformation pattern with a fractal dimension of 1.7, similar to uncharged polymers. …”
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“…SANS intensities show a power law dependence on the scattering vector, q, indicating that the clusters can be described as mass fractal aggregates. The experimentally observed fractal dimension was d = 2.6 ± 0.3. …”
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