Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum measurements, stochastic networks, the uncertainty principle,
  and not so strange "weak values"   The outcomes of a series of measurements, made on a quantum system, form a
sequence of random events which occur in a particular order. The system,
together with a meter or meters, can be seen as following the paths of a
stochastic network connecting all possible outcomes. The paths are shaped from
the virtual paths of the system, and the corresponding probabilities are
determined by the measuring devices employed. If the measurements are highly
accurate, the virtual paths become "real", and the mean values of a quantity (a
functional) is directly related to the frequencies with which the paths are
travelled. If the measurements are highly inaccurate, the mean (weak) values
are expressed in terms of the relative probabilities amplitudes. For pre- and
post-selected systems they are bound to take arbitrary values, depending on the
chosen transition. This is a direct consequence of the uncertainty principle,
which forbids one to distinguish between interfering alternatives, while
leaving the interference between them intact.

25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg