Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exploring group theory and topology for analyzing the structure of
  biology   The concepts of population and species play a fundamental role in biology.
The existence and precise definition of higher-order hierarchies, such as
division into species, is open to debate among biologists. First, we seek to
show a fractal structure of species. We are able to define a species as a
$p$-Sylow subgroup of a particular community in a single niche, confirmed by
topological analysis. We named this model the patch with zeta dominance (PzDom)
model. Next, the topological nature of the system is carefully examined and for
testing purposes, species density data are used in conjunction with data
derived from liquid-chromatography mass spectrometry of proteins. We confirm
the induction of hierarchy and time through a one-dimensional probability space
with certain topologies. For further clarification of induced fractals
including the relation to renormalization in physics, a theoretical development
is proposed based on a newly identified fact, namely that scaling parameters
for magnetization exactly correspond to imaginary parts of the Riemann zeta
function's nontrivial zeros. A master torus and a Lagrangian/Hamiltonian are
derived expressing fractal structures as a solution for diminishing divergent
terms in renormalization. We will also focus on an application of our developed
model. We extend current PzDom model to the so-called exPzDom model to qualify
population dynamics as a topological matter as a whole, not focusing on
hierarchy. The indicators in the exPzDom model adhere well to the empirical
dynamics of SARS-CoV-2 infected people and align appropriately with actual
policies instituted by the Japanese government. In our patch with zeta
dominance (PzDom) model or its extended version (exPzDom), calculations only
require knowledge of the density of individuals over time.

23
The categories of this paper are: solv-int
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom