1,180 research outputs found
Tight Bounds on the R\'enyi Entropy via Majorization with Applications to Guessing and Compression
This paper provides tight bounds on the R\'enyi entropy of a function of a
discrete random variable with a finite number of possible values, where the
considered function is not one-to-one. To that end, a tight lower bound on the
R\'enyi entropy of a discrete random variable with a finite support is derived
as a function of the size of the support, and the ratio of the maximal to
minimal probability masses. This work was inspired by the recently published
paper by Cicalese et al., which is focused on the Shannon entropy, and it
strengthens and generalizes the results of that paper to R\'enyi entropies of
arbitrary positive orders. In view of these generalized bounds and the works by
Arikan and Campbell, non-asymptotic bounds are derived for guessing moments and
lossless data compression of discrete memoryless sources.Comment: The paper was published in the Entropy journal (special issue on
Probabilistic Methods in Information Theory, Hypothesis Testing, and Coding),
vol. 20, no. 12, paper no. 896, November 22, 2018. Online available at
https://www.mdpi.com/1099-4300/20/12/89
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
Quantitative Comparison of Abundance Structures of Generalized Communities: From B-Cell Receptor Repertoires to Microbiomes
The \emph{community}, the assemblage of organisms co-existing in a given
space and time, has the potential to become one of the unifying concepts of
biology, especially with the advent of high-throughput sequencing experiments
that reveal genetic diversity exhaustively. In this spirit we show that a tool
from community ecology, the Rank Abundance Distribution (RAD), can be turned by
the new MaxRank normalization method into a generic, expressive descriptor for
quantitative comparison of communities in many areas of biology. To illustrate
the versatility of the method, we analyze RADs from various \emph{generalized
communities}, i.e.\ assemblages of genetically diverse cells or organisms,
including human B cells, gut microbiomes under antibiotic treatment and of
different ages and countries of origin, and other human and environmental
microbial communities. We show that normalized RADs enable novel quantitative
approaches that help to understand structures and dynamics of complex
generalize communities
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