Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zipf's law, 1/f noise, and fractal hierarchy   Fractals, 1/f noise, Zipf's law, and the occurrence of large catastrophic
events are typical ubiquitous general empirical observations across the
individual sciences which cannot be understood within the set of references
developed within the specific scientific domains. All these observations are
associated with scaling laws and have caused a broad research interest in the
scientific circle. However, the inherent relationships between these scaling
phenomena are still pending questions remaining to be researched. In this
paper, theoretical derivation and mathematical experiments are employed to
reveal the analogy between fractal patterns, 1/f noise, and the Zipf
distribution. First, the multifractal process follows the generalized Zipf's
law empirically. Second, a 1/f spectrum is identical in mathematical form to
Zipf's law. Third, both 1/f spectra and Zipf's law can be converted into a
self-similar hierarchy. Fourth, fractals, 1/f spectra, Zipf's law, and the
occurrence of large catastrophic events can be described with similar
exponential laws and power laws. The self-similar hierarchy is a more general
framework or structure which can be used to encompass or unify different
scaling phenomena and rules in both physical and social systems such as cities,
rivers, earthquakes, fractals, 1/f noise, and rank-size distributions. The
mathematical laws on the hierarchical structure can provide us with a holistic
perspective of looking at complexity such as self-organized criticality (SOC).

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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
1
The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph