A zero-delay sequential scheme for lossy coding of individual sequences

We consider adaptive sequential lossy coding of bounded individual sequences when the performance is measured by the sequentially accumulated mean squared distortion. Theencoder and the decoder are connected via a noiseless channel of capacity $R$ and both are assumed to have zero delay. No probabilistic assumptions are made on how the sequence to be encoded is generated. For any bounded sequence of length $n$, the distortion redundancy is defined as the normalized cumulative distortion of the sequential scheme minus the normalized cumulative distortion of the best scalarquantizer of rate $R$ which is matched to this particular sequence. We demonstrate the existence of a zero-delay sequential scheme which uses common randomization in the encoder and the decoder such that the normalized maximum distortion redundancy converges to zero at a rate $n^{-1/5}\log n$ as the length of the encoded sequence $n$ increases without bound.

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Comprend : Notes de pratique radiologique ; Un cas de calcul salivaire

Articles convenus entre le Roi et le prince-évêque, l'église et l'état de Liège, pour l'exécution du traité du 24 mai 1772 et en conformité de l'article séparé relatif à l'art 1er dudit traité. [Ratification du 11 décembre.]

[Acte royal. 1773-12-11. Versailles]

Evolutionary dynamics of coding and non-coding transcriptomes.

Gene expression changes may underlie much of phenotypic evolution. The development of high-throughput RNA sequencing protocols has opened the door to unprecedented large-scale and cross-species transcriptome comparisons by allowing accurate and sensitive assessments of transcript sequences and expression levels. Here, we review the initial wave of the new generation of comparative transcriptomic studies in mammals and vertebrate outgroup species in the context of earlier work. Together with various large-scale genomic and epigenomic data, these studies have unveiled commonalities and differences in the dynamics of gene expression evolution for various types of coding and non-coding genes across mammalian lineages, organs, developmental stages, chromosomes and sexes. They have also provided intriguing new clues to the regulatory basis and phenotypic implications of evolutionary gene expression changes.