Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Age-dependent Branching Processes and Applications to the
  Luria-Delbr\"uck Experiment   Microbial populations adapt to their environment by acquiring advantageous
mutations, but in the early twentieth century, questions about how these
organisms acquire mutations arose. The experiment of Salvador Luria and Max
Delbr\"uck that won them a Nobel Prize in 1969 confirmed that mutations don't
occur out of necessity, but instead can occur many generations before there is
a selective advantage, and thus organisms follow Darwinian evolution instead of
Lamarckian. Since then, new areas of research involving microbial evolution
have spawned as a result of their experiment. Determining the mutation rate of
a cell is one such area. Probability distributions that determine the number of
mutants in a large population have been derived by D. E. Lea, C. A. Coulson,
and J. B. S. Haldane. However, not much work has been done when time of cell
division is dependent on the cell age, and even less so when cell division is
asymmetric, which is the case in most microbial populations. Using probability
generating function methods, we rigorously construct a probability distribution
for the cell population size given a life-span distribution for both mother and
daughter cells, and then determine its asymptotic growth rate. We use this to
construct a probability distribution for the number of mutants in a large cell
population, which can be used with likelihood methods to estimate the cell
mutation rate.

15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol