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

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

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

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

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

Stochastic self-assembly of incommensurate clusters

We examine the classic problem of homogeneous nucleation and growth by deriving and analyzing a fully discrete stochastic master equation. Upon comparison with results obtained from the corresponding mean-field Becker-D\"{o}ring equations we find striking differences between the two corresponding equilibrium mean cluster concentrations. These discrepancies depend primarily on the divisibility of the total available mass by the maximum allowed cluster size, and the remainder. When such mass incommensurability arises, a single remainder particle can "emulsify" or "disperse" the system by significantly broadening the mean cluster size distribution. This finite-sized broadening effect is periodic in the total mass of the system and can arise even when the system size is asymptotically large, provided the ratio of the total mass to the maximum cluster size is finite. For such finite ratios we show that homogeneous nucleation in the limit of large, closed systems is not accurately described by classical mean-field mass-action approaches.Comment: 5 pages, 4 figures, 1 tabl

The Effect of Acetaminophen on Oxidative Modification of Low-Density Lipoproteins in Hypercholesterolemic Rabbits

Oxidative modification of low-density lipoproteins (LDL) contributes to the pathology of atherosclerosis. Antioxidants may protect LDL against oxidative modification. Acetaminophen, a widely used analgesic and antipyretic agent, has significant antioxidant properties. However, there is little evidence to suggest that acetaminophen acts as an antioxidant for LDL oxidation in vivo. In this study, we investigated the in vivo effect of acetaminophen on LDL oxidation in hypercholesterolemic rabbits. The oxidative modification of LDL was identified by conjugated dienes and thiobarbituric acid-reactive substances (TBARS). In the cholesterol group which rabbits were fed a diet contained 1% g cholesterol for 8 weeks, TBARS contents and conjugated diene levels in the plasma and isolated LDL samples significantly increased compared with the control rabbits (p<0.05). However, in the cholesterol + acetaminophen group, the TBARS contents and conjugated diene levels were significantly lower than that of the cholesterol group (p<0.05). The results from in vitro studies also demonstrated that the LDL isolated from serum was oxidized by Cu++ ions and this oxidation reduced in the presence of acetaminophen. The reduced oxidative modification of LDL by acetaminophen may be of therapeutic value in preventing the development and progression of atherosclerosis

Determining Absorption, Emissivity Reduction, and Local Suppression Coefficients inside Sunspots

The power of solar acoustic waves is reduced inside sunspots mainly due to absorption, emissivity reduction, and local suppression. The coefficients of these power-reduction mechanisms can be determined by comparing time-distance cross-covariances obtained from sunspots and from the quiet Sun. By analyzing 47 active regions observed by SOHO/MDI without using signal filters, we have determined the coefficients of surface absorption, deep absorption, emissivity reduction, and local suppression. The dissipation in the quiet Sun is derived as well. All of the cross-covariances are width corrected to offset the effect of dispersion. We find that absorption is the dominant mechanism of the power deficit in sunspots for short travel distances, but gradually drops to zero at travel distances longer than about 6 degrees. The absorption in sunspot interiors is also significant. The emissivity-reduction coefficient ranges from about 0.44 to 1.00 within the umbra and 0.29 to 0.72 in the sunspot, and accounts for only about 21.5% of the umbra's and 16.5% of the sunspot's total power reduction. Local suppression is nearly constant as a function of travel distance with values of 0.80 and 0.665 for umbrae and whole sunspots respectively, and is the major cause of the power deficit at large travel distances.Comment: 14 pages, 21 Figure