Finite Dimensional Infinite Constellations

In the setting of a Gaussian channel without power constraints, proposed by Poltyrev, the codewords are points in an n-dimensional Euclidean space (an infinite constellation) and the tradeoff between their density and the error probability is considered. The capacity in this setting is the highest achievable normalized log density (NLD) with vanishing error probability. This capacity as well as error exponent bounds for this setting are known. In this work we consider the optimal performance achievable in the fixed blocklength (dimension) regime. We provide two new achievability bounds, and extend the validity of the sphere bound to finite dimensional infinite constellations. We also provide asymptotic analysis of the bounds: When the NLD is fixed, we provide asymptotic expansions for the bounds that are significantly tighter than the previously known error exponent results. When the error probability is fixed, we show that as n grows, the gap to capacity is inversely proportional (up to the first order) to the square-root of n where the proportion constant is given by the inverse Q-function of the allowed error probability, times the square root of 1/2. In an analogy to similar result in channel coding, the dispersion of infinite constellations is 1/2nat^2 per channel use. All our achievability results use lattices and therefore hold for the maximal error probability as well. Connections to the error exponent of the power constrained Gaussian channel and to the volume-to-noise ratio as a figure of merit are discussed. In addition, we demonstrate the tightness of the results numerically and compare to state-of-the-art coding schemes.Comment: 54 pages, 13 figures. Submitted to IEEE Transactions on Information Theor

Cosmological constraints on a light non-thermal sterile neutrino

Although the MiniBooNE experiment has severely restricted the possible existence of light sterile neutrinos, a few anomalies persist in oscillation data, and the possibility of extra light species contributing as a subdominant hot (or warm) component is still interesting. In many models, this species would be in thermal equilibrium in the early universe and share the same temperature as active neutrinos, but this is not necessarily the case. In this work, we fit up-to-date cosmological data with an extended LambdaCDM model, including light relics with a mass typically in the range 0.1 -10 eV. We provide, first, some nearly model-independent constraints on their current density and velocity dispersion, and second, some constraints on their mass, assuming that they consist either in early decoupled thermal relics, or in non-resonantly produced sterile neutrinos. Our results can be used for constraining most particle-physics-motivated models with three active neutrinos and one extra light species. For instance, we find that at the 3 sigma confidence level, a sterile neutrino with mass m_s = 2 eV can be accommodated with the data provided that it is thermally distributed with (T_s/T_nu) < 0.8, or non-resonantly produced with (Delta N_eff) < 0.5. The bounds become dramatically tighter when the mass increases. For m_s < 0.9 eV and at the same confidence level, the data is still compatible with a standard thermalized neutrino.Comment: 18 pages, 6 figure

Flower proteome: changes in protein spectrum during the advanced stages of rose petal development

Flowering is a unique and highly programmed process, but hardly anything is known about the developmentally regulated proteome changes in petals. Here, we employed proteomic technologies to study petal development in rose ( Rosa hybrida ). Using two-dimensional polyacrylamide gel electrophoresis, we generated stage-specific (closed bud, mature flower and flower at anthesis) petal protein maps with ca. 1,000 unique protein spots. Expression analyses of all resolved protein spots revealed that almost 30% of them were stage-specific, with ca. 90 protein spots for each stage. Most of the proteins exhibited differential expression during petal development, whereas only ca. 6% were constitutively expressed. Eighty-two of the resolved proteins were identified by mass spectrometry and annotated. Classification of the annotated proteins into functional groups revealed energy, cell rescue, unknown function (including novel sequences) and metabolism to be the largest classes, together comprising ca. 90% of all identified proteins. Interestingly, a large number of stress-related proteins were identified in developing petals. Analyses of the expression patterns of annotated proteins and their corresponding RNAs confirmed the importance of proteome characterization.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47485/1/425_2005_Article_1512.pd

Rate Distortion Performance in Coding Band-Limited Sources by Sampling and Dithered Quantization

The rate-distortion characteristics of a scheme for encoding continuous-time band-limited stationary sources, with a prescribed band, is considered. In this coding procedure the input is sampled at Nyquist&apos;s rate or faster, the samples undergo dithered uniform or lattice quantization, using subtractive dither, and the quantizer output is entropy coded. The rate-distortion performance, and the trade-off between the sampling rate and the quantization accuracy is investigated, utilizing the observation that the coding scheme is equivalent to an additive noise channel. It is shown that the mean-square error of the scheme is fixed as long as the product of the sampling period and the quantizer second moment is kept constant, while for a fixed distortion the coding rate generally increases when the sampling rate exceeds the Nyquist rate. Finally, as the lattice quantizer dimension becomes large, the equivalent additive noise channel of the scheme tends to be Gaussian, and both the rate and t..

A Generalization of the Entropy Power Inequality with Applications

We prove the following generalization of the Entropy Power Inequality: h(Ax) h(A~x) where h(\Delta) denotes (joint-) differential-entropy, x = x 1 : : : xn is a random vector with independent components, ~ x = ~ x 1 : : : ~ xn is a Gaussian vector with independent components such that h(~x i ) = h(x i ), i = 1 : : : n, and A is any matrix. This generalization of the entropy-power inequality is applied to show that a non-Gaussian vector with independent components becomes &quot;closer&quot; to Gaussianity after a linear transformation, where the distance to Gaussianity is measured by the information divergence. Another application is a lower bound, greater than zero, for the mutual-information between non overlapping spectral components of a non-Gaussian white process. Finally, we describe a dual generalization of the Fisher Information Inequality. Key Words: Entropy Power Inequality, Non-Gaussianity, Divergence, Fisher Information Inequality. This research was supported in part by the Wolf..