Laurent Dumas

• Professor
• Professor (Full) at Versailles Saint-Quentin-en-Yvelines University

The COVID-19 epidemic has highlighted the importance of hospital resource management in exceptional health contexts. The hospital capacity of intensive care units has emerged as a determining factor in overall hospital management. The objective of this study is to create a tool for predicting the saturation status of an intensive care unit. The pre...

The stochastic framework of the NERA model (N: Nonuser, E: Experimental user, R: Recreational user, A: Addict) depicting the dynamics of marijuana usage in the pre and post Initiative-502 (I-502) in Washington, is analysed. Randomness is introduced in (i) the degree of influence that E exerts on N in order to take into account the fluctuations in s...

Since the works of Radon and Cormack on the classical Radon transform on straight lines, several generalizations involving integrations on conical surfaces have been studied. In this article, we introduce a new family of conical surfaces with arbitrary vertices of the space and axes through the origin and study the corresponding Radon transform. We...

Purpose: To evaluate and compare the ocular aberrations in healthy normal eyes with Zernike versus Low Degree/High Degree (LD/HD) coefficients using OPD-Scan III wavefront sampling. Methods: Retrospective case series. Ocular wavefront acquisition using automated skiascopy was performed in mesopic conditions on refractive surgery candidates. Root Me...

Highlights The Omicron SARS-CoV-2 variant of concern is driving the COVID pandemic at a pace never seen before. When the threat of overwhelming healthcare systems balances the hope of achieving herd immunity, providing booster shots and vaccinating fragile individuals can still be attempted in France to prevent death and hospitalizations.

In this paper, we address an alternative formulation for the exact inverse formula of the Radon transform on circle arcs arising in a modality of Compton Scattering Tomography in translational geometry proposed by Webber and Miller (Inverse Problems (36)2, 025007, 2020). The original study proposes a first method of reconstruction, using the theory...

A novel approach depicting the dynamics of marijuana usage to gauge the effects of peer influence in a school population, is the site of investigation. Consumption of drug is considered as a contagious social epidemic which is spread mainly by peer influences. A relation-based graph-CA (r-GCA) model consisting of 4 states namely, Nonusers (N), Expe...

Purpose: The purpose of this study was to compare the low degree/high degree (LD/HD) and Zernike Expansion simulation outcomes evaluating the corneal wavefront changes after theoretical conventional and customized aspheric photorefractive ablations. Methods: Initial anterior corneal surface profiles were modeled as conic sections with pre-operat...

In this paper, we address an alternative formulation for the exact inverse formula of the Radon transform on circle arcs arising in a modality of Compton Scattering Tomography in translational geometry proposed by Webber and Miller (Inverse Problems (36)2, 025007, 2020). The original study proposes a first method of reconstruction, using the theory...

This paper analyses the impact of I-502 implementation in the state of Washington, using the NERA model. The NERA system comprises of 4 classes of users namely, N: nonusers, E: experimental users, R: recreational users and A: addicts. The persistence of illicit drug use is proved when the conditions R0 > 1 and mu > 1 are ensured. Data available in...

We are in the midst of a shift towards using novel polynomials to decompose wavefront aberrations in a more ophthalmologically relevant way. Zernike polynomials have useful mathematical properties but fail to provide clinically relevant wavefront interpretation and predictions. We compared the distribution of the eye's aberrations and demonstrate s...

In material testing applications, Computed Tomography is a well established imaging technique that allows the recovery of the attenuation map of an object. Conventional modalities exploit only primary radiation and although in the energy ranges used in industrial applications Compton scatter radiation is significant, it is removed from the measured...

Purpose: To expand upon and clinically demonstrate the results of a new polynomial decomposition method. Methods: To discuss the theoretical considerations comparing the qualitative and quantitative information produced by the Zernike coefficients and a new polynomial decomposition basis, in a comparative series of theoretical and clinical case...

The in-house Direct Simulation Monte Carlo code (DSMC-IEMC) has been used in Ariane group for more than 30 years to simulate rarefied gas dynamics in hypersonic conditions. In order to improve the accuracy of the simulations, chemical reactions have been implemented. Considering chemical reactions in the DSMC-IEMC code implies new input data taken...

In this paper, we describe an interface reconstruction method in two dimension. This method is an extension of DPIR [1], which reconstructs continuous interfaces and preserves partial volumes using dynamic programming. First we extend the method to curved interfaces. Then, we present tools to improve its robustness in order to apply it to unstructu...

Objects having a flattened geometry, such as those encountered in heritage, have always been difficult to be analysed with conventional X-ray tomography methods due to their anisotropic morphology. To overcome the limitations of classical tomography for such samples, we envisage a new imaging modality based on Compton scattering. While Compton effe...

Zernike circle polynomials are in widespread use for wavefront analysis because of their orthogonality over a circular pupil and their representation of balanced classical aberrations. However, some of the higher-order modes contain linear and quadratic terms. A new aberration series is proposed to better separate the low- versus higher-order aberr...

The optical defects of the human eye are analyzed and classified by studying the corre-sponding ocular wavefront. After presenting the orthogonal basis, called the Zernike basis, which is currently used for the wavefront analysis, a new mathematical decomposition basis is built. In this new basis, the phase errors due to the low degree aberrations...

Contributions to the CIMPA School on mathematical models in biology and medicine

Characterization and interpretation of flat ancient material objects, such as those found in archaeology, paleoenvironments, paleontology, and cultural heritage, have remained a challenging task to perform by means of conventional X-ray tomography methods due to their anisotropic morphology and flattened geometry. To overcome the limitations of the...

A new 2D interface reconstruction method which ensures continuity of the interface and preserves volume fractions is presented here. It is made of two steps, first the minimization of a cost functional based on volume fractions least square errors by using dynamic programming, a fast and efficient scheme well known in image processing, and then a l...

This work aims at quantifying the effect of inherent uncertainties from cardiac output on the sensitivity of a human compliant arterial network response based on stochastic simulations of a reduced-order pulse wave propagation model. A simple pulsatile output form is utilized to reproduce the most relevant cardiac features with a minimum number of...

Cardiovascular diseases are currently the leading cause of mortality in the population of developed countries, due to the constant increase in cardiovascular risk factors. Numerous prospective and retrospective studies have shown that arterial stiffening is a relevant predictor of these diseases. Unfortunately, arterial stiffness distribution acros...

Patrimonial and ancient material objects having a flattened geometry are nowadays difficult to study with classic X-ray tomography methods. Such samples are encountered in both cultural heritage, such as stratigraphical section of paint layers, or in paleontology such as Lagerstatten fossils. To overcome the limitation of classical X-rays tomograph...

Reservoir model needs to be constrained by various data, including dynamic production data. Reservoir heterogeneities are usually described using geostatistical approaches. Constraining geological/geostatistical model realizations by dynamic data is generally performed through history matching, which is a complex inversion process and requires a pa...

Purpose: To evaluate the theoretical influence of the change in corneal asphericity (ΔQ) on the change in fourth-order Zernike spherical aberration coefficient (ΔC(4)0) with customized aspheric refractive correction of myopia and hyperopia. Methods: The initial anterior corneal surface profile was modeled as a conic section of apical radius of c...

History matching is a challenging optimization problem that involves numerous evaluations of a very expensive objective function through the simulation of complex fluids flows inside an oil reservoir. Typically, the gradient of such a function is not always available. Therefore derivative free optimization methods such as Powell's NEWUOA are often...

ive function are in general the output of a complex simulator for which we don’t have any explicit expression. And the absence of any information on the function gradient narrows the resolution field to algorithms using no first or second order derivatives. There exists many different approaches in derivative free optimization, among which the most...

Geostatistical methods are commonly used to characterize oil field heterogeneities in order to establish a predictive reservoir model. To reduce the model uncertainties, dynamic information, such as production or 4D seismic data, are usually integrated in the modelling through history matching. However, despite the growing use of geostatistical met...

The design of structural beams involves the presence of uncertainties in minimizing the cross-sectional area subject to constraints on bending stress, deflection, and bounds. This is a case of robust optimization problem in which solutions are sampled around the neighborhood of a given solution and the mean and variance of this sample are taken as...

Starting from non invasive experimental measurements by Doppler echotracking, the human arterial tree of a given patient is numerically reconstructed.The chosen approach consists in building a simplified fluid/structure interaction model for each artery and to find the parameters of the network by solving an inverse problem. The first reconstructio...

This paper deals with a joint nonuniform illumination estimation and blind deconvolution for barcode signals by using evolutionary algorithms. Indeed, such optimization problems are highly non convex and a robust method is needed in case of noisy and/or blurred signals and nonuniform illumination. Here, we present the construction of a genetic algo...

A new fully adaptive hybrid optimization method (AHM) has been developed and applied to an industrial problem in the field of the aircraft engine industry. The adaptivity of the coupling between a global search by a population-based method (Genetic Algorithms or Evolution Strategies) and the local search by a descent method has been particularly em...

Pour bien comprendre les orientations suivies dans ce mémoire, il convient de replacer les travaux présentés dans leur contexte historique. Au commencement de ce travail, au milieu des années 90, il y eut le projet de navette européenne Hermès et les problèmes associés de réentrée dans la haute atmosphère qui m'orientèrent vers l'étude des modèles...

A stent device is a permanent metallic implant currently used to prop open arteries blocked with atherosclerotic plaques. Many classes of stents are available and mainly differ by their design. Our purpose in this paper is to deter- mine some optimal stent parameters to ensure a conforming blood flow through the stented artery. Coupling compu- tati...

The car drag reduction problem is a major topic in the automotive industry because of its close link with fuel consumption reduction. Until recently, a computational approach of this problem was unattainable because of its complexity and its computational cost. A first attempt in this direction has been presented by the present author as part of a...

In this paper, we propose the use of Genetic Algorithms as a tool for improving a pacemaker efficiency in a defective heart. Such device is generally used when the electrical activity of the heart is deficient and consists in applying electrodes on several points at the surface of the heart. % surface.By optimizing the positions of these electrodes...

A new global optimisation algorithm is presented and applied to the design of high-channel-count multichannel filters based on sampled Fibre Bragg Gratings (FBGs). We focus on the realisation of particular designs corresponding to multichannel filters that consist of 16 and 38 totally reflective identical channels spaced 100 GHz. The results are co...

In this paper, we reformulate global optimization problems in terms of boundary value problems. This allows us to introduce a new class of optimization algorithms. Indeed, many optimization methods, including non-deterministic ones, can be seen as discretizations of initial value problems for differential equations or systems of differential equati...

Various global optimization methods are compared in order to find the best strategy to solve realistic drag reduction problems in the automotive industry. All the methods consist in improving classical genetic algorithms, either by coupling them with a deterministic descent method or by incorporating a fast but approximated evaluation process. The...

Hybrid method for aerodynamic shape optimization in automative industry shape optimization. Various global optimization methods are constructed in order to be able to tackle real- istic drag reduction problems in the automotive industry. All the methods consist in improving classical genetic algorithms, by coupling them with a fast but approximated...

An aerodynamic shape optimization tool for complex industrial flows is developed, based on an hybrid process. The optimization method couples a stochastic genetic algorithm and a deterministic BFGS hill-climbing method. For each evaluation required by the optimizer, the Navier–Stokes equations with the k–ϵ turbulence model are solved with a commerc...

We propose to use a genetic algorithm for optimizing the design of high-channel-count sampled fiber Bragg gratings and show that it leads to better results than classical methods based on a Fourier transform approach.

This article is devoted to the mathematical analysis ofvarious f ormulas giving the equivalent absorption and scattering cross section for mixed materials in linear transport theory. We begin with a general result on the treatment ofhigh-f requency oscillations in linear transport equations which is partly based upon the velocity averaging results...

A simple fluid-structure interaction model for the simulation of blood flow in arteries is studied here. Derived from the general 3D equations, it computes the section area of the artery and the volumetric flux of the flow for each longitudinal position and time. The present article deals with the identification of the main parameters of this model...

This paper presents numerical simulations of slag accumulation in the aft end of a large solid rocket motor. This study has been carried out using technical skills of different companies involved in this program. The objective of this investigation is to analyze how the flow turbulence, in the chamber, can modify the slag accumulation in the motor....

. In this note, we explain in detail how the notion of mean free path is related to the mathematical results obtained in our previous paper [DDG]. Key Words. Mean free path, dispersive billiards, periodic Lorentz gas, kinetic theory, exit time, homogenization. The purpose of this note is to clarify ambiguities concerning the notion of mean free pat...

We study the 2D motion of independent point particles colliding with a periodic array of circular obstacles. The interaction between the particles and the obstacles is described by a total accommodation reflection law. Assuming that the array of scatterers has finite horizon, the density of particles is approximated by the solution of a diffusion e...

We prove theorems pertaining to periodic arrays of spherical, obstacles which show how the macroscopic limit of the mean free path depends on the scaling of the size of the obstacles. We treat separately the cases where the obstacles are totally and partially absorbing, and we also distinguish between two-dimensional arrays, where our results are o...

The purpose of this paper is to show how genetic algorithms can improve the cure of heartbeat pathologies by optimizing the positionning of the electrodes of a pacemaker. A very flrst simulation on a simplifled disease heart is presented and show how electrocardiograms are sensitive to the electrodes positioning.

1. Abstract A 1D model for the simulation of blood ∞ow in arteries is studied here. Derived from the general 3D equations, it computes the section area of the artery and the volumic ∞ux of the ∞ow for each longitu- dinal position and time. The present article deals with the identiflcation of the main parameter of this model linked to the artery com...

In this article we propose a new method in order to solve a general black-box global optimization problem where function evaluations are expensive. Our work was motivated by many problems in the oil industry, coming from several domains like reservoir engineering, molecular modeling, engine calibration and inverse problems in geosciences. Even if e...