Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dispersion for Two Classes of Random Variables: General Theory and
  Application to Inference of an External Ligand Concentration by a Cell   We derive expressions for the dispersion for two classes of random variables
in Markov processes. Random variables like current and activity pertain to the
first class, which is composed by random variables that change whenever a jump
in the stochastic trajectory occurs. The second class corresponds to the time
the trajectory spends in a state (or cluster of states). While the expression
for the first class follows straightforwardly from known results in the
literature, we show that a similar formalism can be used to derive an
expression for the second class. As an application, we use this formalism to
analyze a cellular two-component network estimating an external ligand
concentration. The uncertainty related to this external concentration is
calculated by monitoring different random variables related to an internal
protein. We show that, inter alia, monitoring the time spent in the
phosphorylated state of the protein leads to a finite uncertainty only if there
is dissipation, whereas the uncertainty obtained from the activity of the
transitions of the internal protein can reach the Berg and Purcell limit even
in equilibrium.

22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th