Jean-François Bercher

A common variant in combination with a nonsense mutation in a member of the thioredoxin family causes primary ciliary dyskinesia.

Thioredoxins belong to a large family of enzymatic proteins that function as general protein disulfide reductases, therefore participating in several cellular processes via redox-mediated reactions. So far, none of the 18 members of this family has been involved in human pathology. Here we identified TXNDC3, which encodes a thioredoxin–nucleoside diphosphate kinase, as a gene implicated in primary ciliary dyskinesia (PCD), a genetic condition characterized by chronic respiratory tract infections, left–right asymmetry randomization, and male infertility. We show that the disease, which segregates as a recessive trait, results from the unusual combination of the following two transallelic defects: a nonsense mutation and a common intronic variant found in 1% of control chromosomes. This variant affects the ratio of two physiological TXNDC3 transcripts: the full-length isoform and a novel isoform, TXNDC3d7, carrying an in-frame deletion of exon 7. In vivo and in vitro expression data unveiled the physiological importance of TXNDC3d7 (whose expression was reduced in the patient) and the corresponding protein that was shown to bind microtubules. PCD is known to result from defects of the axoneme, an organelle common to respiratory cilia, embryonic nodal cilia, and sperm flagella, containing dynein arms, with, to date, the implication of genes encoding dynein proteins. Our findings, which identify a another class of molecules involved in PCD, disclose the key role of TXNDC3 in ciliary function; they also point to an unusual mechanism underlying a Mendelian disorder, which is an SNP-induced modification of the ratio of two physiological isoforms generated by alternative splicing.

Estimating the entropy of a signal with applications

We present a new estimator of the entropy of continuous signals. We model the unknown probability density of data in the form of an AR spectrum density and use regularized long-AR models to identify the AR parameters. We then derive both an analytical expression and a practical procedure for estimating the entropy from sample data. We indicate how to incorporate recursive and adaptive features in the procedure. We evaluate and compare the new estimator with other estimators based on histograms, kernel density models, and order statistics. Finally, we give several examples of applications. An adaptive version of our entropy estimator is applied to detection of law changes, blind deconvolution, and source separation.

Analysis of signals in the Fisher–Shannon information plane

We show that the analysis of complex, possibly non-stationary signals, can be carried out in an information plane, defined by both Shannon entropy and Fisher information. Our study is exemplified by two large families of distributions with physical relevance: the Student-t and the power exponentials.  2003 Elsevier Science B.V. All rights reserved.

On some entropy functionals derived from Rényi information divergence

We consider the maximum entropy problems associated with Renyi Q-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the generalized expectation as encountered in nonextensive statistics. The optimum maximum entropy probability distributions, which can exhibit a power-law behaviour, are derived and characterized. The Renyi entropy of the optimum distributions can be viewed as a function of the constraint. This defines two families of entropy functionals in the space of possible expected values. General properties of these functionals, including nonnegativity, minimum, convexity, are documented. Their relationships as well as numerical aspects are also discussed. Finally, we work out some specific cases for the reference measure Q(x) and recover in a limit case some well-known entropies.

Source Coding with Escort Distributions and Rényi Entropy Bounds

We discuss the interest of escort distributions and Renyi entropy in the context of source coding. We first recall a source coding theorem by Campbell relating a generalized measure of length to the Renyi-Tsallis entropy. We show that the associated optimal codes can be obtained using considerations on escort-distributions. We propose a new family of measure of length involving escort-distributions and we show that these generalized lengths are also bounded below by the Renyi entropy. Furthermore, we obtain that the standard Shannon codes lengths are optimum for the new generalized lengths measures, whatever the entropic index. Finally, we show that there exists in this setting an interplay between standard and escort distributions.

On minimum Fisher information distributions with restricted support and fixed variance

Fisher information is of key importance in estimation theory. It also serves in inference problems as well as in the interpretation of many physical processes. The mean-squared estimation error for the location parameter of a distribution is bounded by the inverse of the Fisher information associated with this distribution. In this paper we look for minimum Fisher information distributions with a restricted support. More precisely, we study the problem of minimizing the Fisher information in the set of distributions with fixed variance defined on a bounded subset S of R or on the positive real line. We show that the solutions of the underlying differential equation can be expressed in terms of Whittaker functions. Then, in the two considered cases, we derive the explicit expressions of the solutions and investigate their behavior. We also characterize the behavior of the minimum Fisher information as a function of the imposed variance.

Some properties of generalized Fisher information in the context of nonextensive thermostatistics

We present two extended forms of Fisher information that fit well in the context of nonextensive thermostatistics. We show that there exists an interplay between these generalized Fisher information, the generalized q-Gaussian distributions and the q-entropies. The minimum of the generalized Fisher information among distributions with a fixed moment, or with a fixed q-entropy is attained, in both cases, by a generalized q-Gaussian distribution. This complements the fact that the q-Gaussians maximize the q-entropies subject to a moment constraint, and yields new variational characterizations of the generalizedq-Gaussians. We show that the generalized Fisher information naturally pop up in the expression of the time derivative of the q-entropies, for distributions satisfying a certain nonlinear heat equation. This result includes as a particular case the classical de Bruijn identity. Then we study further properties of the generalized Fisher information and of their minimization. We show that, though non additive, the generalized Fisher information of a combined system is upper bounded. In the case of mixing, we show that the generalized Fisher information is convex for q≥1. Finally, we show that the minimization of the generalized Fisher information subject to moment constraints satisfies a Legendre structure analog to the Legendre structure of thermodynamics.

A simple probabilistic construction yielding generalized entropies and divergences, escort distributions and q-Gaussians

We give a simple probabilistic description of a transition between two states which leads to a generalized escort distribution. When the parameter of the distribution varies, it defines a parametric curve that we call an escort-path. The Renyi divergence appears as a natural by-product of the setting. We study the dynamics of the Fisher information on this path, and show in particular that the thermodynamic divergence is proportional to Jeffreys’ divergence. Next, we consider the problem of inferring a distribution on the escort-path, subject to generalized moment constraints. We show that our setting naturally induces a rationale for the minimization of the Renyi information divergence. Then, we derive the optimum distribution as a generalized q-Gaussian distribution.

Design, optimization and calibration of an HFB-based ADC

We describe the design of an HFB-based ADC targeted towards the digitization of a very large band for Software Defined Radio applications. We present an original procedure for the optimization of the synthesis filters, when the front-end analysis filters use standard low-cost analog filters. We also address the calibration of the device, namely the identification of the actual analog filters, and highlight the impact of the identification and of measurement errors on the overall performances.

Design, optimization and realization of an HFB-based ADC

This paper presents a two-channel Hybrid Filter Bank (HFB) Analog-to-Digital Converter (ADC) that targets broadband digitization, for Cognitive Radio (CR) applications. The proposed architecture partitioning uses low-cost third order Butterworth analog filters and fourth order digital IIR filters. The optimization algorithm combines direct simplex search, minimax methods and a perturbation strategy to avoid local minima. A sensitivity study of the analog filters quantifies the impact of poles and zeros spread on system performance. Finally, the experimental results obtained from our concrete realization are reported. The measurements show the aliasing rejection provided by HFB structure and confirms the parallel architecture sensitivity to analog mismatches.