Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-scale structural complexity of natural patterns   Complexity of patterns is a key information for human brain to differ objects
of about the same size and shape. Like other innate human senses, the
complexity perception cannot be easily quantified. We propose a transparent and
universal machine method for estimating structural (effective) complexity of
two- and three-dimensional patterns that can be straightforwardly generalized
onto other classes of objects. It is based on multi-step renormalization of the
pattern of interest and computing the overlap between neighboring renormalized
layers. This way, we can define a single number characterizing the structural
complexity of an object. We apply this definition to quantify complexity of
various magnetic patterns and demonstrate that not only does it reflect the
intuitive feeling of what is "complex" and what is "simple", but also can be
used to accurately detect different phase transitions and gain information
about dynamics of non-equilibrium systems. When employed for that, the proposed
scheme is much simpler and numerically cheaper than the standard methods based
on computing correlation functions or using machine learning techniques.

25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
19
The categories of this paper are: eess
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an