Volume-preserving geometric shape optimization of the Dirichlet energy using variational neural networks.

In this work, we explore the numerical solution of geometric shape optimization problems using neural network-based approaches. This involves minimizing a numerical criterion that includes solving a partial differential equation with respect to a domain, often under geometric constraints like a constant volume. We successfully develop a proof of concept using a flexible and parallelizable methodology to tackle these problems.

Vector-borne disease outbreak control via instant releases.

This paper is devoted to the study of optimal release strategies to control vector-borne diseases, such as dengue, Zika, chikungunya and malaria. Two techniques are considered: the sterile insect one (SIT), which consists in releasing sterilized males among wild vectors in order to perturb their reproduction, and the Wolbachia one (presently used mainly for mosquitoes), which consists in releasing vectors, that are infected with a bacterium limiting their vectorial capacity, in order to replace the wild population by one with reduced vectorial capacity. In each case, the time dynamics of the vector population is modeled by a system of ordinary differential equations in which the releases are represented by linear combinations of Dirac measures with positive coefficients determining their intensity.

Optimal Immunity Control and Final Size Minimization by Social Distancing for the SIR Epidemic Model.

The aim of this article is to understand how to apply partial or total containment to SIR epidemic model during a given finite time interval in order to minimize the epidemic final size, that is the cumulative number of cases infected during the complete course of an epidemic. The existence and uniqueness of an optimal strategy are proved for this infinite-horizon problem, and a full characterization of the solution is provided. The best policy consists in applying the maximal allowed social distancing effort until the end of the interval, starting at a date that is not always the closest date and may be found by a simple algorithm.

Mosquito population control strategies for fighting against arboviruses.

In the fight against vector-borne arboviruses, an important strategy of control of epidemic consists in controlling the population of the vector, mosquitoes in this case. Among possible actions, two techniques consist either in releasing sterile mosquitoes to reduce the size of the population (Sterile Insect Technique) or in replacing the wild population by one carrying a bacteria, called blocking the transmission of viruses from insects to humans. This article addresses the issue of optimizing the dissemination protocol for each of these strategies, in order to get as close as possible to these objectives.

Clinical efficacy and safety comparison of adapalene gel and tretinoin gel in the treatment of acne vulgaris: Europe and U.S. multicenter trials.

Background: Adapalene is a new chemical entity that exhibits tretinoin-like activities in the terminal differentiation process.

Objective: We evaluated a dose range effect of two concentrations of adapalene gel as acne treatment and compared adapalene 0.1% gel with tretinoin 0.