Among the different indicators that quantify the spread of an epidemic such as the on-going COVID-19, stands first the reproduction number which measures how many people can be contaminated by an infected person. In order to permit the monitoring of the evolution of this number, a new estimation procedure is proposed here, assuming a well-accepted model for current incidence data, based on past observations. The novelty of the proposed approach is twofold: 1) the estimation of the reproduction number is achieved by convex optimization within a proximal-based inverse problem formulation, with constraints aimed at promoting piecewise smoothness; 2) the approach is developed in a multivariate setting, allowing for the simultaneous handling of multiple time series attached to different geographical regions, together with a spatial (graph-based) regularization of their evolutions in time. The effectiveness of the approach is first supported by simulations, and two main applications to real COVID-19 data are then discussed. The first one refers to the comparative evolution of the reproduction number for a number of countries, while the second one focuses on French departments and their joint analysis, leading to dynamic maps revealing the temporal co-evolution of their reproduction numbers.

Texture characterization of photographic prints can provide scholars with valuable information regarding photographers? aesthetic intentions and working practices. Currently, texture assessment is strictly based on the visual acuity of a range of scholars associated with collecting institutions, such as museum curators and conservators. Natural interindividual discrepancies, intraindividual variability, and the large size of collections present a pressing need for computerized and automated solutions for the texture characterization and classification of photographic prints. In the this article, this challenging image processing task is addressed using an anisotropic multiscale representation of texture, the hyperbolic wavelet transform (HWT), from which robust multiscale features are constructed. Cepstral distances aimed at ensuring balanced multiscale contributions are computed between pairs of images. The resulting large-size affinity matrix is then clustered using spectral clustering, followed by a Ward linkage procedure. For proof of concept, these procedures are first applied to a reference data set of historic photographic papers that combine several levels of similarity and second to a large data set of culturally valuable photographic prints held by the Museum of Modern Art in New York. The characterization and clustering results are interpreted in collaboration with art scholars with an aim toward developing new modes of art historical research and humanities-based collaboration.

Daily pandemic surveillance, often achieved through the estimation of the reproduction number, constitutes a critical challenge for national health authorities to design counter-measures. In an earlier work, we proposed to formulate the estimation of the reproduction number as an optimization problem, combining data-model fidelity and space-time regularity constraints, solved by nonsmooth convex proximal minimizations. Though promising, that first formulation significantly lacks robustness against the Covid-19 data low quality (irrelevant or missing counts, pseudo-seasonalities,...) stemming from the emergency and crisis context, which significantly impairs accurate pandemic evolution assessments. The present work aims to overcome these limitations by carefully crafting a functional permitting to estimate jointly, in a single step, the reproduction number and outliers defined to model low quality data. This functional also enforces epidemiology-driven regularity properties for the reproduction number estimates, while preserving convexity, thus permitting the design of efficient minimization algorithms, based on proximity operators that are derived analytically. The explicit convergence of the proposed algorithm is proven theoretically. Its relevance is quantified on real Covid-19 data, consisting of daily new infection counts for 200+ countries and for the 96 metropolitan France counties, publicly available at Johns Hopkins University and Santé-Publique-France. The procedure permits automated daily updates of these estimates, reported via animated and interactive maps. Open-source estimation procedures will be made publicly available.

We describe how to analyze the wide class of non-stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability distributions. These ersatz versions of entropy, mutual information, and entropy rate can be estimated when only a single realization of the process is available. We abundantly illustrate our approach by analyzing Gaussian and non-Gaussian self-similar signals, as well as multi-fractal signals. Using Gaussian signals allows us to check that our approach is robust in the sense that all quantities behave as expected from analytical derivations. Using the stationarity (independence on the integration time) of the ersatz entropy rate, we show that this quantity is not only able to fine probe the self-similarity of the process, but also offers a new way to quantify the multi-fractality.

Intrapartum fetal heart rate (FHR) monitoring constitutes a reference tool in clinical practice to assess the baby’s health status and to detect fetal acidosis. It is usually analyzed by visual inspection grounded on FIGO criteria. Characterization of intrapartum fetal heart rate temporal dynamics remains a challenging task and continuously receives academic research efforts. Complexity measures, often implemented with tools referred to as approximate entropy (ApEn) or sample entropy (SampEn), have regularly been reported as significant features for intrapartum FHR analysis. We explore how information theory, and especially auto-mutual information (AMI), is connected to ApEn and SampEn and can be used to probe FHR dynamics. Applied to a large (1404 subjects) and documented database of FHR data, collected in a French academic hospital, it is shown that (i) auto-mutual information outperforms ApEn and SampEn for acidosis detection in the first stage of labor and continues to yield the best performance in the second stage; (ii) Shannon entropy increases as labor progresses and is always much larger in the second stage; (iii) babies suffering from fetal acidosis additionally show more structured temporal dynamics than healthy ones and that this progressive structuration can be used for early acidosis detection.