Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal fits of diffusion constants from single time data points of
  Brownian trajectories   Experimental methods based on single particle tracking (SPT) are being
increasingly employed in the physical and biological sciences, where nanoscale
objects are visualized with high temporal and spatial resolution. SPT can probe
interactions between a particle and its environment but the price to be paid is
the absence of ensemble averaging and a consequent lack of statistics. Here we
address the benchmark question of how to accurately extract the diffusion
constant of one single Brownian trajectory. We analyze a class of estimators
based on weighted functionals of the square displacement. For a certain choice
of the weight function these functionals provide the true ensemble averaged
diffusion coefficient, with a precision that increases with the trajectory
resolution.

28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc