“…Greater complexity (increased fractal dimensions) was clearly discernable by light microscopy for stained sections of fixed samples that had been conditioned compared to various controls. …”
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“…Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. …”
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“…Here we report the molecular realization, using two-dimensional self-assembly of DNA tiles, of a cellular automaton whose update rule computes the binary function XOR and thus fabricates a fractal pattern—a Sierpinski triangle—as it grows. …”
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“…Color and spatial information extracted from chromatic co-occurrence matrix and mass fractal dimension were used as well. Finally, the experimental results in a real mission demonstrate the validity of the proposed methodologies and the performances of the algorithms.…”
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“…We compared the performance of the proposed method with that of three state‐of‐the‐art methods, namely, the radial gradient index filtering technique, the local mean technique, and the fractal dimension technique. We conclude that the proposed method is more accurate and performs more effectively than do the benchmark algorithms considered. …”
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“…To study the effects of grain size on the tensile strength and toughness of rock samples, a modified fracture model was established linking fictitious crack to the grain size so that the microstructure of the specimens and fictitious crack growth can be considered together. The fractal method was introduced to represent microstructure of three kinds of granites and used to determine the length of fictitious crack. …”
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“…The average scores in normalized aesthetic measures of Benford's law, fractal dimension, global contrast factor, and Shannon's entropy are 0.630, 0.397, 0.418, and 0.708, respectively. …”
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“…This study constructed S–E relationships for a specific RAD, which indicated that if the community had a fractal distribution of rank abundance, E would decrease with S, and the S–E relationship would be unique for a given RAD. …”
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“…This novel non-contact electrostatic method has been used to assess the particle stimulus-responsive wettability in detail. Video footage and fractal analysis were used in conjunction with a two-stage model to characterize the kinetics of transfer of particles to a water droplet surface, and internalization of particles by the droplet. …”
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“…Various diagnostic techniques are used to analyze retinal microvasculature image to enable geometric features measurements such as vessel tortuosity, branching angles, branching coefficient, vessel diameter, and fractal dimension. These extracted markers or characterized fundus digital image features provide insights and relates quantitative retinal vascular topography abnormalities to various pathologies such as diabetic retinopathy, macular degeneration, hypertensive retinopathy, transient ischemic attack, neovascular glaucoma, and cardiovascular diseases. …”
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“…The paper is based largely upon a critical review of the literature, but includes a more quantitative, physics-based analysis of velocity strengthening and a new analysis of velocity weakening that incorporates parameters that describe the (proposed) fractal character of the sliding interface. This article is part of the theme issue ‘Modelling of sea-ice phenomena’.…”
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“…This led to the definition of scaling laws that described the organisation of landscapes under fluvial incision and were later explored by statistical physics and fractal mathematics. The emblematic Hack’s Law proposes a power-law relationship between watershed area and main stream length. …”
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“…The surface morphology of the films was found to be composed of pores formed by aggregates of EW molecules, both with a fractal form. An increase in the number of film layers resulted in the increase of the number of pores up to a maximum value followed by a decrease. …”
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“…Lamellar assembly with fractal-patterned growth into dendritic and ringed spherulites of crystallized poly(l-lactic acid) (PLLA), of two molecular weight (MW) grades and crystallized at (temperature of crystallization) T(c) = 120 and 130 °C, respectively, are evaluated using optical and atomic-force microscopies. …”
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“…The gelation time increased as the PLA chain length increased. In addition, the fractal dimension of each gel was close to that of a percolation cluster. …”
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“…In contrast, we did not find strong bias effects from perceptually novel fractal images, as would be predicted if novel items induce a learning mode that then biases recognition judgments. …”
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“…METHODS: We specifically investigated the complexity of cortical folding, a measure of cortical neurodevelopment, employing a novel method to quantify local fractal dimension (FD) measures that uses spherical harmonic reconstructions. …”
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“…Then, we quantify structural differences between the graphs extracted from the groups of healthy and non-healthy patients. We also use fractal analysis to characterize the extracted graphs. …”
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“…The results obtained show that the fouling layer at the slow TMP-increase stage possessed a higher average roughness (71.27 nm) and increased fractal dimension (2.33), which resulted in a low membrane fouling rate (0.87 kPa/d). …”
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“…We therefore examined three human perceptions well-established in previous NLS studies (“Complexity,” “Pleasantness,” and “Familiarity”), and the accuracy of identification, for a large NLS database and related these four measures to objective spectro-temporal NLS features, defined using rigorous mathematical descriptors including stimulus entropic and algorithmic complexity measures, peaks-related measures, fractal dimension estimates, and various spectral measures (mean spectral centroid, power in discrete frequency ranges, harmonicity, spectral flatness, and spectral structure). …”
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