Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Highly optimized tolerance and power laws in dense and sparse resource
  regimes   Power law cumulative frequency $(P)$ vs. event size $(l)$ distributions
$P(\geq l)\sim l^{-\alpha}$ are frequently cited as evidence for complexity and
serve as a starting point for linking theoretical models and mechanisms with
observed data. Systems exhibiting this behavior present fundamental
mathematical challenges in probability and statistics. The broad span of length
and time scales associated with heavy tailed processes often require special
sensitivity to distinctions between discrete and continuous phenomena. A
discrete Highly Optimized Tolerance (HOT) model, referred to as the
Probability, Loss, Resource (PLR) model, gives the exponent $\alpha=1/d$ as a
function of the dimension $d$ of the underlying substrate in the sparse
resource regime. This agrees well with data for wildfires, web file sizes, and
electric power outages. However, another HOT model, based on a continuous
(dense) distribution of resources, predicts $\alpha= 1+ 1/d $. In this paper we
describe and analyze a third model, the cuts model, which exhibits both
behaviors but in different regimes. We use the cuts model to show all three
models agree in the dense resource limit. In the sparse resource regime, the
continuum model breaks down, but in this case, the cuts and PLR models are
described by the same exponent.

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The categories of this paper are: plasm-ph
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio