Multiresolution vector quantization

Multiresolution source codes are data compression algorithms yielding embedded source descriptions. The decoder of a multiresolution code can build a source reproduction by decoding the embedded bit stream in part or in whole. All decoding procedures start at the beginning of the binary source description and decode some fraction of that string. Decoding a small portion of the binary string gives a low-resolution reproduction; decoding more yields a higher resolution reproduction; and so on. Multiresolution vector quantizers are block multiresolution source codes. This paper introduces algorithms for designing fixed- and variable-rate multiresolution vector quantizers. Experiments on synthetic data demonstrate performance close to the theoretical performance limit. Experiments on natural images demonstrate performance improvements of up to 8 dB over tree-structured vector quantizers. Some of the lessons learned through multiresolution vector quantizer design lend insight into the design of more sophisticated multiresolution codes

Automated design of bacterial genome sequences

Background: Organisms have evolved ways of regulating transcription to better adapt to varying environments. Could the current functional genomics data and models support the possibility of engineering a genome with completely rearranged gene organization while the cell maintains its behavior under environmental challenges? How would we proceed to design a full nucleotide sequence for such genomes? Results: As a first step towards answering such questions, recent work showed that it is possible to design alternative transcriptomic models showing the same behavior under environmental variations than the wild-type model. A second step would require providing evidence that it is possible to provide a nucleotide sequence for a genome encoding such transcriptional model. We used computational design techniques to design a rewired global transcriptional regulation of Escherichia coli, yet showing a similar transcriptomic response than the wild-type. Afterwards, we “compiled” the transcriptional networks into nucleotide sequences to obtain the final genome sequence. Our computational evolution procedure ensures that we can maintain the genotype-phenotype mapping during the rewiring of the regulatory network. We found that it is theoretically possible to reorganize E. coli genome into 86% fewer regulated operons. Such refactored genomes are constituted by operons that contain sets of genes sharing around the 60% of their biological functions and, if evolved under highly variable environmental conditions, have regulatory networks, which turn out to respond more than 20% faster to multiple external perturbations. Conclusions: This work provides the first algorithm for producing a genome sequence encoding a rewired transcriptional regulation with wild-type behavior under alternative environments

Quantization as Histogram Segmentation: Optimal Scalar Quantizer Design in Network Systems

An algorithm for scalar quantizer design on discrete-alphabet sources is proposed. The proposed algorithm can be used to design fixed-rate and entropy-constrained conventional scalar quantizers, multiresolution scalar quantizers, multiple description scalar quantizers, and Wyner–Ziv scalar quantizers. The algorithm guarantees globally optimal solutions for conventional fixed-rate scalar quantizers and entropy-constrained scalar quantizers. For the other coding scenarios, the algorithm yields the best code among all codes that meet a given convexity constraint. In all cases, the algorithm run-time is polynomial in the size of the source alphabet. The algorithm derivation arises from a demonstration of the connection between scalar quantization, histogram segmentation, and the shortest path problem in a certain directed acyclic graph

Network vector quantization

We present an algorithm for designing locally optimal vector quantizers for general networks. We discuss the algorithm's implementation and compare the performance of the resulting "network vector quantizers" to traditional vector quantizers (VQs) and to rate-distortion (R-D) bounds where available. While some special cases of network codes (e.g., multiresolution (MR) and multiple description (MD) codes) have been studied in the literature, we here present a unifying approach that both includes these existing solutions as special cases and provides solutions to previously unsolved examples