The Cauchy Distribution in Information Theory.

The Gaussian law reigns supreme in the information theory of analog random variables. This paper showcases a number of information theoretic results which find elegant counterparts for Cauchy distributions. New concepts such as that of equivalent pairs of probability measures and the strength of real-valued random variables are introduced here and shown to be of particular relevance to Cauchy distributions.

Error Exponents and -Mutual Information.

Over the last six decades, the representation of error exponent functions for data transmission through noisy channels at rates below capacity has seen three distinct approaches: (1) Through Gallager's functions (with and without cost constraints); (2) large deviations form, in terms of conditional relative entropy and mutual information; (3) through the -mutual information and the Augustin-Csiszár mutual information of order derived from the Rényi divergence[...

Empirical Estimation of Information Measures: A Literature Guide.

We give a brief survey of the literature on the empirical estimation of entropy, differential entropy, relative entropy, mutual information and related information measures. While those quantities are of central importance in information theory, universal algorithms for their estimation are increasingly important in data science, machine learning, biology, neuroscience, economics, language, and other experimental sciences.

A Forward-Reverse Brascamp-Lieb Inequality: Entropic Duality and Gaussian Optimality.

Inspired by the forward and the reverse channels from the image-size characterization problem in network information theory, we introduce a functional inequality that unifies both the Brascamp-Lieb inequality and Barthe's inequality, which is a reverse form of the Brascamp-Lieb inequality. For Polish spaces, we prove its equivalent entropic formulation using the Legendre-Fenchel duality theory. Capitalizing on the entropic formulation, we elaborate on a "doubling trick" used by Lieb and Geng-Nair to prove the Gaussian optimality in this inequality for the case of Gaussian reference measures.

A Coding Theorem for f-Separable Distortion Measures.

In this work we relax the usual separability assumption made in rate-distortion literature and propose f -separable distortion measures, which are well suited to model non-linear penalties. The main insight behind f -separable distortion measures is to define an -letter distortion measure to be an f -mean of single-letter distortions. We prove a rate-distortion coding theorem for stationary ergodic sources with f -separable distortion measures, and provide some illustrative examples of the resulting rate-distortion functions.

Exfoliative cytology and titanium dental implants: a pilot study.

Background: Oral exfoliative cytology is a diagnostic method that involves the study of cells exfoliated from the oral mucosa. Ions/particles released from metallic implants can remain in the peri-implant milieu. The aim of the present study is to assess the presence of metal particles in cells exfoliated from peri-implant oral mucosa around titanium dental implants.