29,643 research outputs found
MaxEnt power spectrum estimation using the Fourier transform for irregularly sampled data applied to a record of stellar luminosity
The principle of maximum entropy is applied to the spectral analysis of a
data signal with general variance matrix and containing gaps in the record. The
role of the entropic regularizer is to prevent one from overestimating
structure in the spectrum when faced with imperfect data. Several arguments are
presented suggesting that the arbitrary prefactor should not be introduced to
the entropy term. The introduction of that factor is not required when a
continuous Poisson distribution is used for the amplitude coefficients. We
compare the formalism for when the variance of the data is known explicitly to
that for when the variance is known only to lie in some finite range. The
result of including the entropic measure factor is to suggest a spectrum
consistent with the variance of the data which has less structure than that
given by the forward transform. An application of the methodology to example
data is demonstrated.Comment: 15 pages, 13 figures, 1 table, major revision, final version,
Accepted for publication in Astrophysics & Space Scienc
Reconstruction of motional states of neutral atoms via MaxEnt principle
We present a scheme for a reconstruction of states of quantum systems from
incomplete tomographic-like data. The proposed scheme is based on the Jaynes
principle of Maximum Entropy. We apply our algorithm for a reconstruction of
motional quantum states of neutral atoms. As an example we analyze the
experimental data obtained by the group of C. Salomon at the ENS in Paris and
we reconstruct Wigner functions of motional quantum states of Cs atoms trapped
in an optical lattice
- …