57,964 research outputs found
Radiation Transfer in the Cavity and Shell of Planetary Nebulae
We develop an approximate analytical solution for the transfer of
line-averaged radiation in the hydrogen recombination lines for the ionized
cavity and molecular shell of a spherically symmetric planetary nebula. The
scattering problem is treated as a perturbation, using a mean intensity derived
from a scattering-free solution. The analytical function was fitted to Halpha
and Hbeta data from the planetary nebula NGC6537. The position of the maximum
in the intensity profile produced consistent values for the radius of the
cavity as a fraction of the radius of the dusty nebula: 0.21 for Halpha and
0.20 for Hbeta. Recovered optical depths were broadly consistent with observed
optical extinction in the nebula, but the range of fit parameters in this case
is evidence for a clumpy distribution of dust.Comment: MNRAS accepted; 10 Fig
Variable dimension weighted universal vector quantization and noiseless coding
A new algorithm for variable dimension weighted universal coding is introduced. Combining the multi-codebook system of weighted universal vector quantization (WUVQ), the partitioning technique of variable dimension vector quantization, and the optimal design strategy common to both, variable dimension WUVQ allows mixture sources to be effectively carved into their component subsources, each of which can then be encoded with the codebook best matched to that source. Application of variable dimension WUVQ to a sequence of medical images provides up to 4.8 dB improvement in signal to quantization noise ratio over WUVQ and up to 11 dB improvement over a standard full-search vector quantizer followed by an entropy code. The optimal partitioning technique can likewise be applied with a collection of noiseless codes, as found in weighted universal noiseless coding (WUNC). The resulting algorithm for variable dimension WUNC is also described
One-pass adaptive universal vector quantization
The authors introduce a one-pass adaptive universal quantization technique for real, bounded alphabet, stationary sources. The algorithm is set on line without any prior knowledge of the statistics of the sources which it might encounter and asymptotically achieves ideal performance on all sources that it sees. The system consists of an encoder and a decoder. At increasing intervals, the encoder refines its codebook using knowledge about incoming data symbols. This codebook is then described to the decoder in the form of updates on the previous codebook. The accuracy to which the codebook is described increases as the number of symbols seen, and thus the accuracy to which the codebook is known, grows
Universal quantization of parametric sources has redundancy k/2 (log n)/n
Rissanen has shown that there exist universal noiseless codes for {Xi} with per-letter rate redundancy as low as k/2 (log n)/n, where n is the blocklength and k is the number of source parameters. We derive an analogous result for universal quantization: for any given La-grange multiplier λ>0, there exist universal fixed-rate and variable-rate quantizers with per-letter Lagrangian redundancy (i.e., distortion redundancy plus λ times the rate redundancy) as low as λk/2 (log n)/n
Variable-rate source coding theorems for stationary nonergodic sources
For a stationary ergodic source, the source coding theorem and its converse imply that the optimal performance theoretically achievable by a fixed-rate or variable-rate block quantizer is equal to the distortion-rate function, which is defined as the infimum of an expected distortion subject to a mutual information constraint. For a stationary nonergodic source, however, the. Distortion-rate function cannot in general be achieved arbitrarily closely by a fixed-rate block code. We show, though, that for any stationary nonergodic source with a Polish alphabet, the distortion-rate function can be achieved arbitrarily closely by a variable-rate block code. We also show that the distortion-rate function of a stationary nonergodic source has a decomposition as the average of the distortion-rate functions of the source's stationary ergodic components, where the average is taken over points on the component distortion-rate functions having the same slope. These results extend previously known results for finite alphabets
Rates of convergence in adaptive universal vector quantization
We consider the problem of adaptive universal quantization. By adaptive quantization we mean quantization for which the delay associated with encoding the jth sample in a sequence of length n is bounded for all n>j. We demonstrate the existence of an adaptive universal quantization algorithm for which any weighted sum of the rate and the expected mean square error converges almost surely and in expectation as O(√(log log n/log n)) to the corresponding weighted sum of the rate and the distortion-rate function at that rate
AdS Strings with Torsion: Non-complex Heterotic Compactifications
Combining the effects of fluxes and gaugino condensation in heterotic
supergravity, we use a ten-dimensional approach to find a new class of
four-dimensional supersymmetric AdS compactifications on almost-Hermitian
manifolds of SU(3) structure. Computation of the torsion allows a
classification of the internal geometry, which for a particular combination of
fluxes and condensate, is nearly Kahler. We argue that all moduli are fixed,
and we show that the Kahler potential and superpotential proposed in the
literature yield the correct AdS radius. In the nearly Kahler case, we are able
to solve the H Bianchi using a nonstandard embedding. Finally, we point out
subtleties in deriving the effective superpotential and understanding the
heterotic supergravity in the presence of a gaugino condensate.Comment: 42 pages; v2. added refs, revised discussion of Bianchi for N
Cation Transport in Polymer Electrolytes: A Microscopic Approach
A microscopic theory for cation diffusion in polymer electrolytes is
presented. Based on a thorough analysis of molecular dynamics simulations on
PEO with LiBF the mechanisms of cation dynamics are characterised. Cation
jumps between polymer chains can be identified as renewal processes. This
allows us to obtain an explicit expression for the lithium ion diffusion
constant D_{Li} by invoking polymer specific properties such as the Rouse
dynamics. This extends previous phenomenological and numerical approaches. In
particular, the chain length dependence of D_{Li} can be predicted and compared
with experimental data. This dependence can be fully understood without
referring to entanglement effects.Comment: 4 pages, 4 figures, Physical Review Letters in pres
Strong latitudinal shear in the shallow convection zone of a rapidly rotating A-star
We have derived the mean broadening profile of the star V102 in the region of
the open cluster IC4665 from high resolution spectroscopy. At a projected
equatorial rotation velocity of vsini = (105 +- 12)km/s we find strong
deviation from classical rotation. We discuss several scenarios, the most
plausible being strong differential rotation in latitudinal direction. For this
scenario we find a difference in angular velocity of DeltaOmega = 3.6 +- 0.8
rad/d (DeltaOmega/Omega = 0.42 +- 0.09). From the Halpha line we derive a
spectral type of A9 and support photometric measurements classifying IC4665
V102 as a non-member of IC4665. At such early spectral type this is the
strongest case of differential rotation observed so far. Together with three
similar stars, IC4665 V102 seems to form a new class of objects that exhibit
extreme latitudinal shear in a very shallow convective envelope.Comment: accepted for A&A Letter
A vector quantization approach to universal noiseless coding and quantization
A two-stage code is a block code in which each block of data is coded in two stages: the first stage codes the identity of a block code among a collection of codes, and the second stage codes the data using the identified code. The collection of codes may be noiseless codes, fixed-rate quantizers, or variable-rate quantizers. We take a vector quantization approach to two-stage coding, in which the first stage code can be regarded as a vector quantizer that “quantizes” the input data of length n to one of a fixed collection of block codes. We apply the generalized Lloyd algorithm to the first-stage quantizer, using induced measures of rate and distortion, to design locally optimal two-stage codes. On a source of medical images, two-stage variable-rate vector quantizers designed in this way outperform standard (one-stage) fixed-rate vector quantizers by over 9 dB. The tail of the operational distortion-rate function of the first-stage quantizer determines the optimal rate of convergence of the redundancy of a universal sequence of two-stage codes. We show that there exist two-stage universal noiseless codes, fixed-rate quantizers, and variable-rate quantizers whose per-letter rate and distortion redundancies converge to zero as (k/2)n -1 log n, when the universe of sources has finite dimension k. This extends the achievability part of Rissanen's theorem from universal noiseless codes to universal quantizers. Further, we show that the redundancies converge as O(n-1) when the universe of sources is countable, and as O(n-1+ϵ) when the universe of sources is infinite-dimensional, under appropriate conditions
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