8,362 research outputs found
Discontinuities in the Maximum-Entropy Inference
We revisit the maximum-entropy inference of the state of a finite-level
quantum system under linear constraints. The constraints are specified by the
expected values of a set of fixed observables. We point out the existence of
discontinuities in this inference method. This is a pure quantum phenomenon
since the maximum-entropy inference is continuous for mutually commuting
observables. The question arises why some sets of observables are distinguished
by a discontinuity in an inference method which is still discussed as a
universal inference method. In this paper we make an example of a discontinuity
and we explain a characterization of the discontinuities in terms of the
openness of the (restricted) linear map that assigns expected values to states.Comment: 8 pages, 3 figures, 32nd International Workshop on Bayesian Inference
and Maximum Entropy Methods in Science and Engineering, Garching, Germany,
15-20 July 201
Recurrence and algorithmic information
In this paper we initiate a somewhat detailed investigation of the
relationships between quantitative recurrence indicators and algorithmic
complexity of orbits in weakly chaotic dynamical systems. We mainly focus on
examples.Comment: 26 pages, no figure
Function reconstruction as a classical moment problem: A maximum entropy approach
We present a systematic study of the reconstruction of a non-negative
function via maximum entropy approach utilizing the information contained in a
finite number of moments of the function. For testing the efficacy of the
approach, we reconstruct a set of functions using an iterative entropy
optimization scheme, and study the convergence profile as the number of moments
is increased. We consider a wide variety of functions that include a
distribution with a sharp discontinuity, a rapidly oscillatory function, a
distribution with singularities, and finally a distribution with several spikes
and fine structure. The last example is important in the context of the
determination of the natural density of the logistic map. The convergence of
the method is studied by comparing the moments of the approximated functions
with the exact ones. Furthermore, by varying the number of moments and
iterations, we examine to what extent the features of the functions, such as
the divergence behavior at singular points within the interval, is reproduced.
The proximity of the reconstructed maximum entropy solution to the exact
solution is examined via Kullback-Leibler divergence and variation measures for
different number of moments.Comment: 20 pages, 17 figure
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