Are neurons multifractals?

Fernández, Eduardo; Bolea, Jose A.; Ortega, Guillermo J.; Louis, E.

doi:10.1016/s0165-0270(99)00066-7

Cited by 51 publications

(34 citation statements)

References 18 publications

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“…Is a DLA a multifractal? [26,[28][29][30] . These publications and their authors are well known in the fi eld of physics and thus their results are widely cited.…”

Section: How Can Fractal Analysis Be Better Understood?mentioning

confidence: 99%

Understanding Fractal Analysis? The Case of Fractal Linguistics

Jelinek

Jones

Warfel³

et al. 2006

ComPlexUs

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Terms such as ‘self-similarity’, ‘space filling’, ‘fractal dimension’, and associated concepts have different meanings to different people depending on their background. We examine how methodology in fractal analysis is influenced by diverse definitions of fundamental concepts that lead to difficulties in understanding fundamental issues. The meaning of terms associated with fractal analysis needs to be clarified if this method is to be useful in diverse disciplines. It is our premise that communications that are result focused constitute a danger in perpetuating misconceptions of terms due to the concise nature of the writing and the reliance on references to fill in the procedural and conceptual gaps. Communicating effectively requires a sound understanding of the terminology and a clear and meaningful presentation. We address here communication and the nature of scientific discourse, ‘fractal linguistics’.

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“…Is a DLA a multifractal? [26,[28][29][30] . These publications and their authors are well known in the fi eld of physics and thus their results are widely cited.…”

Section: How Can Fractal Analysis Be Better Understood?mentioning

confidence: 99%

Understanding Fractal Analysis? The Case of Fractal Linguistics

Jelinek

Jones

Warfel³

et al. 2006

ComPlexUs

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“…Reliable estimates for the mass fractal dimension can be obtained using this approach based on about 10% of the aggregate particles as centres 2 . As an aside we note that the application of this formalism to neuronal morphology in reference 8 incorrectly uses the exponent q on the left hand side of Eq. (2) rather than the exponent (q − 1).…”

Section: Mi(l)mentioning

confidence: 99%

“…The cumulative mass method has been used extensively in the fractal analysis of clusters grown using computer growth models such as diffusion-limited aggregation 1,2,3,4 , in which the growing aggregates are composed of identical sized particles. The cumulative mass method has also been employed in the fractal analysis of neuronal morphology 5,6,7,8 . In these studies, neuronal morphology has been represented as digitized camera lucida images which can again be regarded as aggregates comprising identical sized particles (pixels).…”

Section: Introductionmentioning

confidence: 99%

Fractal Analysis of Aggregates of Non-Uniformly Sized Particles: An Application to Macaque Monkey Cortical Pyramidal Neurons

Henry¹,

Hof²,

Rothnie³

et al. 2002

Emergent Nature

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“…In our results, an anomalous behaviour is observed: the D q curves increase at the beginning. This anomalous behaviour has also been observed in Opheusden et al (1996), Smith andLange (1998), andFernández et al (1999). Some reasons for this behaviour have been suggested, including that the boxes contain few elements (Fernández et al, 1999), or the small scaling regime covers less than a decade so that we cannot extrapolate the box counting results for the partition function to zero box size (Opheusden et al, 1996).…”

Section: Remarkmentioning

confidence: 67%

Multifractal analysis of solar flare indices and their horizontal visibility graphs

Anh

Eastes

et al. 2012

Nonlin. Processes Geophys.

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Abstract. The multifractal properties of the daily solar Xray brightness, X l and X s , during the period from 1 January 1986 to 31 December 2007 which includes two solar cycles are examined using the universal multifractal approach and multifractal detrended fluctuation analysis. Then we convert these time series into networks using the horizontal visibility graph technique. Multifractal analysis of the resulting networks is performed using an algorithm proposed by us. The results from the multifractal analysis show that multifractality exists in both raw daily time series of X-ray brightness and their horizontal visibility graphs. It is also found that the empirical K(q) curves of raw time series can be fitted by the universal multifractal model. The numerical results on the raw data show that the Solar Cycle 23 is weaker than the Solar Cycle 22 in multifractality. The values of h(2) from multifractal detrended fluctuation analysis for these time series indicate that they are stationary and persistent, and the correlations in the time series of Solar Cycle 23 are stronger than those for Solar Cycle 22. Furthermore, the multifractal scaling for the networks of the time series can reflect some properties which cannot be picked up by using the same analysis on the original time series. This suggests a potentially useful method to explore geophysical data.

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Are neurons multifractals?

Cited by 51 publications

References 18 publications

Understanding Fractal Analysis? The Case of Fractal Linguistics

Understanding Fractal Analysis? The Case of Fractal Linguistics

Fractal Analysis of Aggregates of Non-Uniformly Sized Particles: An Application to Macaque Monkey Cortical Pyramidal Neurons

Multifractal analysis of solar flare indices and their horizontal visibility graphs

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