99,307 research outputs found
Hartle-Hawking state is a maximum of entanglement entropy
It is shown that the Hartle-Hawking state of a scalar field is a maximum of
entanglement entropy in the space of pure quantum states satisfying the
condition that backreaction is finite. In other words, the Hartle-Hawking state
is a curved-space analogue of the EPR state, which is also a maximum of
entanglement entropy.Comment: Latex, 4 pages, Some comments are added on the "small backreaction
condition
The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics
We discuss methods to analyze a quantum Gibbs family in the ultra-cold regime
where the norm closure of the Gibbs family fails due to discontinuities of the
maximum-entropy inference. The current discussion of maximum-entropy inference
and irreducible correlation in the area of quantum phase transitions is a major
motivation for this research. We extend a representation of the irreducible
correlation from finite temperatures to absolute zero.Comment: 8 pages, 3 figures, 34th International Workshop on Bayesian Inference
and Maximum Entropy Methods in Science and Engineering, 21-26 September 2014,
Ch\^ateau du Clos Luc\'e, Amboise, Franc
Maximum entropy properties of discrete-time first-order stable spline kernel
The first order stable spline (SS-1) kernel is used extensively in
regularized system identification. In particular, the stable spline estimator
models the impulse response as a zero-mean Gaussian process whose covariance is
given by the SS-1 kernel. In this paper, we discuss the maximum entropy
properties of this prior. In particular, we formulate the exact maximum entropy
problem solved by the SS-1 kernel without Gaussian and uniform sampling
assumptions. Under general sampling schemes, we also explicitly derive the
special structure underlying the SS-1 kernel (e.g. characterizing the
tridiagonal nature of its inverse), also giving to it a maximum entropy
covariance completion interpretation. Along the way similar maximum entropy
properties of the Wiener kernel are also given
Multi-Scale CLEAN deconvolution of radio synthesis images
Radio synthesis imaging is dependent upon deconvolution algorithms to
counteract the sparse sampling of the Fourier plane. These deconvolution
algorithms find an estimate of the true sky brightness from the necessarily
incomplete sampled visibility data. The most widely used radio synthesis
deconvolution method is the CLEAN algorithm of Hogbom. This algorithm works
extremely well for collections of point sources and surprisingly well for
extended objects. However, the performance for extended objects can be improved
by adopting a multi-scale approach. We describe and demonstrate a conceptually
simple and algorithmically straightforward extension to CLEAN that models the
sky brightness by the summation of components of emission having different size
scales. While previous multiscale algorithms work sequentially on decreasing
scale sizes, our algorithm works simultaneously on a range of specified scales.
Applications to both real and simulated data sets are given.Comment: Submitted to IEEE Special Issue on Signal Processin
Parameters estimation for spatio-temporal maximum entropy distributions: application to neural spike trains
We propose a numerical method to learn Maximum Entropy (MaxEnt) distributions
with spatio-temporal constraints from experimental spike trains. This is an
extension of two papers [10] and [4] who proposed the estimation of parameters
where only spatial constraints were taken into account. The extension we
propose allows to properly handle memory effects in spike statistics, for large
sized neural networks.Comment: 34 pages, 33 figure
Time and spectral domain relative entropy: A new approach to multivariate spectral estimation
The concept of spectral relative entropy rate is introduced for jointly
stationary Gaussian processes. Using classical information-theoretic results,
we establish a remarkable connection between time and spectral domain relative
entropy rates. This naturally leads to a new spectral estimation technique
where a multivariate version of the Itakura-Saito distance is employed}. It may
be viewed as an extension of the approach, called THREE, introduced by Byrnes,
Georgiou and Lindquist in 2000 which, in turn, followed in the footsteps of the
Burg-Jaynes Maximum Entropy Method. Spectral estimation is here recast in the
form of a constrained spectrum approximation problem where the distance is
equal to the processes relative entropy rate. The corresponding solution
entails a complexity upper bound which improves on the one so far available in
the multichannel framework. Indeed, it is equal to the one featured by THREE in
the scalar case. The solution is computed via a globally convergent matricial
Newton-type algorithm. Simulations suggest the effectiveness of the new
technique in tackling multivariate spectral estimation tasks, especially in the
case of short data records.Comment: 32 pages, submitted for publicatio
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