Information In The Non-Stationary Case

Information estimates such as the ``direct method'' of Strong et al. (1998) sidestep the difficult problem of estimating the joint distribution of response and stimulus by instead estimating the difference between the marginal and conditional entropies of the response. While this is an effective estimation strategy, it tempts the practitioner to ignore the role of the stimulus and the meaning of mutual information. We show here that, as the number of trials increases indefinitely, the direct (or ``plug-in'') estimate of marginal entropy converges (with probability 1) to the entropy of the time-averaged conditional distribution of the response, and the direct estimate of the conditional entropy converges to the time-averaged entropy of the conditional distribution of the response. Under joint stationarity and ergodicity of the response and stimulus, the difference of these quantities converges to the mutual information. When the stimulus is deterministic or non-stationary the direct estimate of information no longer estimates mutual information, which is no longer meaningful, but it remains a measure of variability of the response distribution across time

A 3D radiative transfer framework: X. Arbitrary Velocity Fields in the Co-moving Frame

3-D astrophysical atmospheres will have random velocity fields. We seek to combine the methods we have developed for solving the 1-D problem with arbitrary flows to those that we have developed for solving the fully 3-D relativistic radiative transfer problem in the case of monotonic flows. The methods developed in the case of 3-D atmospheres with monotonic flows, solving the fully relativistic problem along curves defined by an affine parameter, are very flexible and can be extended to the case of arbitrary velocity fields in 3-D. Simultaneously, the techniques we developed for treating the 1-D problem with arbitrary velocity fields are easily adapted to the 3-D problem. The algorithm we present allows the solution of 3-D radiative transfer problems that include arbitrary wavelength couplings. We use a quasi-analytic formal solution of the radiative transfer equation that significantly improves the overall computation speed. We show that the approximate lambda operator developed in previous work gives good convergence, even neglecting wavelength coupling. Ng acceleration also gives good results. We present tests that are of similar resolution to what has been presented using Monte-Carlo techniques, thus our methods will be applicable to problems outside of our test setup. Additional domain decomposition parallelization strategies will be explored in future work.Comment: 9 pages, 9 figures, A&A, in press, new version matches copy edited version, definition restore

Remarks on the Theory of Cosmological Perturbation

It is shown that the power spectrum defined in the Synchronous Gauge can not be directly used to calculate the predictions of cosmological models on the large-scale structure of universe, which should be calculated directly by a suitable gauge-invariant power spectrum or the power spectrum defined in the Newtonian Gauge.Comment: 13 pages, 1 figure, minor changes, to be published in Chinese Physics Letter

First Principles Study of Work Functions of Double Wall Carbon Nanotubes

Using first-principles density functional calculations, we investigated work functions (WFs) of thin double-walled nanotubes (DWNTs) with outer tube diameters ranging from 1nm to 1.5nm. The results indicate that work function change within this diameter range can be up to 0.5 eV, even for DWNTs with same outer diameter. This is in contrast with single-walled nanotubes (SWNTs) which show negligible WF change for diameters larger than 1nm. We explain the WF change and related charge redistribution in DWNTs using charge equilibration model (CEM). The predicted work function variation of DWNTs indicates a potential difficulty in their nanoelectronic device applications.Comment: 11 pages, 3 figures, to appear as rapid communication on Physical Review

Scalar emission in a rotating G\"{o}del black hole

We study the absorption probability and Hawking radiation of the scalar field in the rotating G\"{o}del black hole in minimal five-dimensional gauged supergravity. We find that G\"{o}del parameter $j$ imprints in the greybody factor and Hawking radiation. It plays a different role from the angular momentum of the black hole in the Hawking radiation and super-radiance. These information can help us know more about rotating G\"{o}del black holes in minimal five-dimensional gauged supergravity.Comment: 14 pages, 4 figures, This version accepted for publication in Phys. Rev. D contains a minor modification and two new reference