Quantizing rare random maps: application to flooding visualization

Visualization is an essential operation when assessing the risk of rare events such as coastal or river floodings. The goal is to display a few prototype events that best represent the probability law of the observed phenomenon, a task known as quantization. It becomes a challenge when data is expensive to generate and critical events are scarce, like extreme natural hazard. In the case of floodings, each event relies on an expensive-to-evaluate hydraulic simulator which takes as inputs offshore meteo-oceanic conditions and dyke breach parameters to compute the water level map. In this article, Lloyd's algorithm, which classically serves to quantize data, is adapted to the context of rare and costly-to-observe events. Low probability is treated through importance sampling, while Functional Principal Component Analysis combined with a Gaussian process deal with the costly hydraulic simulations. The calculated prototype maps represent the probability distribution of the flooding events in a minimal expected distance sense, and each is associated to a probability mass. The method is first validated using a 2D analytical model and then applied to a real coastal flooding scenario. The two sources of error, the metamodel and the importance sampling, are evaluated to quantify the precision of the method.Comment: 40 pages, 11 Figures, submitted to Journal of Computational and Graphical Statisti

FunQuant: A R package to perform quantization in the context of rare events and time-consuming simulations

Quantization summarizes continuous distributions by calculating a discrete approximation. Among the widely adopted methods for data quantization is Lloyd's algorithm, which partitions the space into Vorono\"i cells, that can be seen as clusters, and constructs a discrete distribution based on their centroids and probabilistic masses. Lloyd's algorithm estimates the optimal centroids in a minimal expected distance sense, but this approach poses significant challenges in scenarios where data evaluation is costly, and relates to rare events. Then, the single cluster associated to no event takes the majority of the probability mass. In this context, a metamodel is required and adapted sampling methods are necessary to increase the precision of the computations on the rare clusters.Comment: 7 pages, 4 figures. Submitted to Journal Of Open Source Softwar

An ancient dental gene network regulates development and continuous regeneration of teeth in sharks

The appearance of toothed vertebrates has proven a major determinant of the overall success of this lineage. This is most apparent in sharks and rays (elasmobranchs), which further retain the capacity for life-long tooth regeneration. Given their comparatively basal phylogenetic position, elasmobranchs therefore offer the opportunity for crucial insights into putative ancestral characters of tooth development, yet despite their evolutionary significance this remains poorly understood. Using the established chondrichthyan model, the catshark (Scyliorhinus sp.), we identified the expression of genes representative of conserved signaling pathways during stages of early dental competence, tooth initiation and regeneration. The expression patterns of β-catenin, shh, bmp4, pax9, pitx1/2, and the stem cell marker Sox2, characterise an ancestrally conserved gene set deployed during initiation of the elasmobranch dentition, suggesting that all vertebrate dentitions are defined by the expression of this core set of genes. These findings provide novel evidence to support the conservation in deep evolutionary time of a core set of dental patterning genes, therefore further defining the evolutionary trajectory of tooth development. We show how these genes facilitate the emergence of the shark dentition and offer insights into their deployment during development of the dental lamina, a sheet of dental epithelial cells that are responsible for continuous tooth regeneration. This study further promotes a specific experimental agenda to further characterise the roles of these core developmental genes during vertebrate tooth development, and importantly dental regeneration

Plans d'expériences: Plans associés à la régression linéaire

Engineering schoo

Plans d'expériences: Plans associés à la régression linéaire

Engineering schoo

Plans d'expériences pour simulations numériques

Engineering schoo

Plans d'expériences pour simulations numériques

Engineering schoo

Introduction to Global Optimization

MasterThese slides constitute a 12h introductory course on global optimization.The course starts with basic concepts specific to global optimization and different from those underlying local optimization algorithms.A selection of 6 algorithms is then presented: random search, randomly restarted local searches, simulated annealing, CMA-ES and Bayesian Optimization. This selection is meant to cover the main mechanisms behind global searches.Pre-requisites are: linear algebra, basic probabilities and local optimization (gradient methods, necessary optimality conditions)

Introduction to Global Optimization

MasterThese slides constitute a 12h introductory course on global optimization.The course starts with basic concepts specific to global optimization and different from those underlying local optimization algorithms.A selection of 6 algorithms is then presented: random search, randomly restarted local searches, simulated annealing, CMA-ES and Bayesian Optimization. This selection is meant to cover the main mechanisms behind global searches.Pre-requisites are: linear algebra, basic probabilities and local optimization (gradient methods, necessary optimality conditions)

Introduction to Global Optimization

MasterThese slides constitute a 12h introductory course on global optimization.The course starts with basic concepts specific to global optimization and different from those underlying local optimization algorithms.A selection of 6 algorithms is then presented: random search, randomly restarted local searches, simulated annealing, CMA-ES and Bayesian Optimization. This selection is meant to cover the main mechanisms behind global searches.Pre-requisites are: linear algebra, basic probabilities and local optimization (gradient methods, necessary optimality conditions)