arXiv subjects

Olivier Bernard

Publications and source records attributed to Olivier Bernard.

At least 37 records · Page 2Linked to original sources

arXiv2023

On analytical theories for conductivity and self-diffusion in concentrated electrolytes

Describing analytically the transport properties of electrolytes, such as their conductivity or the self-diffusion of the ions, has been a central challenge of chemical physics for almost a century. In recent years, this question has regained some interest in light of Stochastic Density Field Theory (SDFT) -- an analytical framework that allows the approximate determination of density correlations in fluctuating systems. In spite of the success of this theory to describe dilute electrolytes, its extension to concentrated solutions raises a number of technical difficulties, and requires simplified descriptions of the short-range repulsion between the ions. In this article, we discuss recent approximations that were proposed to compute the conductivity of electrolytes, in particular truncations of Coulomb interactions at short distances. We extend them to another observable (the self-diffusion coefficient of the ions) and compare them to earlier analytical approaches, such as the mean spherical approximation and mode-coupling theory. We show how the treatment of hydrodynamic effects in SDFT can be improved, that the choice of the modified Coulomb interactions significantly affects the determination of the properties of the electrolytes, and that comparison with other theories provides a guide to extend SDFT approaches in this context.

cond-mat.soft↗

arXiv2023

Phase Unwrapping of Color Doppler Echocardiography using Deep Learning

Color Doppler echocardiography is a widely used non-invasive imaging modality that provides real-time information about the intracardiac blood flow. In an apical long-axis view of the left ventricle, color Doppler is subject to phase wrapping, or aliasing, especially during cardiac filling and ejection. When setting up quantitative methods based on color Doppler, it is necessary to correct this wrapping artifact. We developed an unfolded primal-dual network to unwrap (dealias) color Doppler echocardiographic images and compared its effectiveness against two state-of-the-art segmentation approaches based on nnU-Net and transformer models. We trained and evaluated the performance of each method on an in-house dataset and found that the nnU-Net-based method provided the best dealiased results, followed by the primal-dual approach and the transformer-based technique. Noteworthy, the primal-dual network, which had significantly fewer trainable parameters, performed competitively with respect to the other two methods, demonstrating the high potential of deep unfolding methods. Our results suggest that deep learning-based methods can effectively remove aliasing artifacts in color Doppler echocardiographic images, outperforming DeAN, a state-of-the-art semi-automatic technique. Overall, our results show that deep learning-based methods have the potential to effectively preprocess color Doppler images for downstream quantitative analysis.

eess.IV↗

arXiv2023

Computing $e$-th roots in number fields

We describe several algorithms for computing $e$-th roots of elements in a number field $K$, where $e$ is an odd prime-power integer. In particular we generalize Couveignes' and Thomé's algorithms originally designed to compute square-roots in the Number Field Sieve algorithm for integer factorization. Our algorithms cover most cases of $e$ and $K$ and allow to obtain reasonable timings even for large degree number fields and large exponents $e$. The complexity of our algorithms is better than general root finding algorithms and our implementation compared well in performance to these algorithms implemented in well-known computer algebra softwares. One important application of our algorithms is to compute the saturation phase in the Twisted-PHS algorithm for computing the Ideal-SVP problem over cyclotomic fields in post-quantum cryptography.

math.NT↗

arXiv2023

Extraction of volumetric indices from echocardiography: which deep learning solution for clinical use?

Deep learning-based methods have spearheaded the automatic analysis of echocardiographic images, taking advantage of the publication of multiple open access datasets annotated by experts (CAMUS being one of the largest public databases). However, these models are still considered unreliable by clinicians due to unresolved issues concerning i) the temporal consistency of their predictions, and ii) their ability to generalize across datasets. In this context, we propose a comprehensive comparison between the current best performing methods in medical/echocardiographic image segmentation, with a particular focus on temporal consistency and cross-dataset aspects. We introduce a new private dataset, named CARDINAL, of apical two-chamber and apical four-chamber sequences, with reference segmentation over the full cardiac cycle. We show that the proposed 3D nnU-Net outperforms alternative 2D and recurrent segmentation methods. We also report that the best models trained on CARDINAL, when tested on CAMUS without any fine-tuning, still manage to perform competitively with respect to prior methods. Overall, the experimental results suggest that with sufficient training data, 3D nnU-Net could become the first automated tool to finally meet the standards of an everyday clinical device.

eess.IV↗

arXiv2022

CRISP - Reliable Uncertainty Estimation for Medical Image Segmentation

Accurate uncertainty estimation is a critical need for the medical imaging community. A variety of methods have been proposed, all direct extensions of classification uncertainty estimations techniques. The independent pixel-wise uncertainty estimates, often based on the probabilistic interpretation of neural networks, do not take into account anatomical prior knowledge and consequently provide sub-optimal results to many segmentation tasks. For this reason, we propose CRISP a ContRastive Image Segmentation for uncertainty Prediction method. At its core, CRISP implements a contrastive method to learn a joint latent space which encodes a distribution of valid segmentations and their corresponding images. We use this joint latent space to compare predictions to thousands of latent vectors and provide anatomically consistent uncertainty maps. Comprehensive studies performed on four medical image databases involving different modalities and organs underlines the superiority of our method compared to state-of-the-art approaches.

eess.IV↗

arXiv2022

Optimal periodic resource allocation in reactive dynamical systems: Application to microalgal production

In this article, we focus on a periodic resource allocation problem applied to a dynamical system which comes from a biological system. More precisely, we consider a system with $N$ resources and $N$ activities, each activity use the allocated resource to evolve up to a given time $T > 0$ where a control (represented by a given permutation) will be applied on the system to reallocate the resources. The goal is to find the optimal control strategies which optimize the cost or the benefit of the system. This problem can be illustrated by an industrial biological application, namely, the optimization of a mixing strategy to enhance the growth rate in a microalgal raceway system. A mixing device, such as a paddle wheel, is considered to control the rearrangement of the depth of the algae cultures, hence the light perceived at each lap. We prove that if the dynamics of the system is periodic, then the period corresponds to one reallocation whatever the order of the involved permutation matrix is. A nonlinear optimization problem for one reallocation process is then introduced. Since $N!$ permutations need to be tested in the general case, it can be numerically solved only for a limited number of $N$. To overcome this difficulty, we introduce a second optimization problem which provides a suboptimal solution of the initial problem, but whose solution can be determined explicitly. A sufficient condition to characterize cases where the two problems have the same solution is given. Some numerical experiments are performed to assess the benefit of optimal strategies in various settings.

math.NA↗

arXiv2022

Echocardiography Segmentation with Enforced Temporal Consistency

Convolutional neural networks (CNN) have demonstrated their ability to segment 2D cardiac ultrasound images. However, despite recent successes according to which the intra-observer variability on end-diastole and end-systole images has been reached, CNNs still struggle to leverage temporal information to provide accurate and temporally consistent segmentation maps across the whole cycle. Such consistency is required to accurately describe the cardiac function, a necessary step in diagnosing many cardiovascular diseases. In this paper, we propose a framework to learn the 2D+time apical long-axis cardiac shape such that the segmented sequences can benefit from temporal and anatomical consistency constraints. Our method is a post-processing that takes as input segmented echocardiographic sequences produced by any state-of-the-art method and processes it in two steps to (i) identify spatio-temporal inconsistencies according to the overall dynamics of the cardiac sequence and (ii) correct the inconsistencies. The identification and correction of cardiac inconsistencies relies on a constrained autoencoder trained to learn a physiologically interpretable embedding of cardiac shapes, where we can both detect and fix anomalies. We tested our framework on 98 full-cycle sequences from the CAMUS dataset, which are available alongside this paper. Our temporal regularization method not only improves the accuracy of the segmentation across the whole sequences, but also enforces temporal and anatomical consistency.

eess.IV↗

arXiv2021

Physics-constrained intraventricular vector flow mapping by color Doppler

Color Doppler by transthoracic echocardiography creates 2-D fan-shaped maps of blood velocities in the cardiac cavities. It is a one-component velocimetric technique since it only returns the velocity components parallel to the ultrasound beams. Intraventricular vector flow mapping (iVFM) is a method to recover the blood velocity vectors from the Doppler scalar fields in an echocardiographic three-chamber view. We improved our iVFM numerical scheme by imposing physical constraints. The iVFM consisted in minimizing regularized Doppler residuals subject to the condition that two fluid-dynamics constraints were satisfied, namely planar mass conservation, and free-slip boundary conditions. The optimization problem was solved by using the Lagrange multiplier method. A finite-difference discretization of the optimization problem, written in the polar coordinate system centered on the cardiac ultrasound probe, led to a sparse linear system. The single regularization parameter was determined automatically for non-supervision considerations. The physics-constrained method was validated using realistic intracardiac flow data from a patient-specific CFD model. The numerical evaluations showed that the iVFM-derived velocity vectors were in very good agreement with the CFD-based original velocities, with relative errors ranged between 0.3 and 12%. We calculated two macroscopic measures of flow in the cardiac region of interest, the mean vorticity and mean stream function, and observed an excellent concordance between physics-constrained iVFM and CFD. The capability of physics-constrained iVFM was finally tested with in vivo color Doppler data acquired in patients routinely examined in the echocardiographic laboratory. The vortex that forms during the rapid filling was deciphered. The physics-constrained iVFM algorithm is ready for pilot clinical studies.

physics.med-ph↗

arXiv2021

A short basis of the Stickelberger ideal of a cyclotomic field

We exhibit an explicit short basis of the Stickelberger ideal of cyclotomic fields of any conductor $m$, i.e., a basis containing only short elements. By definition, an element of $\mathbb{Z}[G_m]$, where $G_m$ denotes the Galois group of the field, is called short whenever it writes as $\sum_{σ\in G_m} \varepsilon_σσ$ with all $\varepsilon_σ\in\{0,1\}$. One ingredient for building such a basis consists in picking wisely generators $α_m(b)$ in a large family of short elements. As a direct practical consequence, we deduce from this short basis an explicit upper bound on the relative class number, that is valid for any conductor. This basis also has several concrete applications, in particular for the cryptanalysis of the Shortest Vector Problem on Ideal lattices.

math.NT↗

arXiv2021

Optimal optical conditions for Microalgal production in photobioreactors

The potential of industrial applications for microalgae has motivated their recent fast development. Their growth dynamics depends on different factors that must be optimized. Since they get their energy from photosynthesis, light is a key factor that strongly influences their productivity. Light is absorbed and scattered in the liquid medium, and irradiance exponentially decreases towards the darkest part of the photobioreactor at a rate nonlinearly depending on the biomass concentration. Maximizing productivity is then a tricky problem, especially when the growth rate is inhibited by an excess of light. Productivity optimization turns out to be highly dependent on how light is distributed along the reactor, and is therefore related to the extinction rate and the background turbidity. The concept of optical depth productivity is introduced for systems where background turbidity must be accounted for and a global optimum maximizing productivity is proposed, extending the concept of the compensation condition. This optimal condition consists in compensating the algal growth rate at the bottom of the reactor by the respiration. This condition can drive the optimization of the surface biomass productivity depending on the minimum reachable depth. We develop a nonlinear controller and prove the global asymptotic stability of the biomass concentration towards the desired optimal value.

math.NA↗

arXiv2020

Mixing strategies combined with shape design to enhance productivity of a raceway pond

This paper focuses on mixing strategies and designing shape of the bottom topographies to enhance the growth of the microalgae in raceway ponds. A physical-biological coupled model is used to describe the growth of the algae. A simple model of a mixing device such as a paddle wheel is also considered. The complete process model was then included in an optimization problem associated with the maximization of the biomass production. The results show that non-trivial topographies can be coupled with some specific mixing strategies to improve the microalgal productivity.

math.NA↗

arXiv2020

Optimizing microalgal productivity in raceway ponds through a controlled mixing device

This paper focuses on mixing strategies to enhance the growth of microalgae in a raceway pond. The flow is assumed to be laminar and the Han model describing the dynamics of the photosystems is used as a basis to determine growth rate as a function of light history. A device controlling the mixing is assumed, which means that the order of the cells along the different layers can be rearranged at each new lap according to a permutation matrix P. The order of cell depth hence the light perceived is consequently modified on a cyclical basis. The dynamics of the photosystems are computed over K laps of the raceway with permutation P. It is proven that if a periodic regime is reached, it will be periodic immediately after the first lap, which enables to reduce significantly the computational cost when testing all the permutations. In view of optimizing the production, a functional corresponding to the average growth rate along depth and for one lap is introduced. A suboptimal but explicit solution is proposed and compared numerically to the optimal permutation and other strategies for different cases. Finally, the expected gains in growth rate are discussed.

math.OC↗

arXiv2020

Controlling the bottom topography of a microalgal pond to optimize productivity

We present a coupled model describing growth of microalgae in a raceway cultivation process, accounting for hydrodynamics. Our approach combines a biological model (based on the Han model) and shallow water dynamics equations that model the fluid into the raceway. We then describe an optimization procedure dealing with the topography to maximize the biomass production over one cycle (one lap of the raceway). The results show that non-flat topographies enhance microalgal productivity.

math.OC↗

arXiv2020

Spectral mapping of polarization-correlated photon-pair sources using quantum-classical correspondence

Direct spectral characterization of a quantum photon-pair source usually involves cumbersome, costly, and time-consuming detection issues. In this study, we experimentally characterize the spectral properties of a type-II phase-matched spontaneous parametric down-conversion (SPDC) source based on a titanium-diffused periodically poled lithium niobate (Ti:PPLN) waveguide. The characterization of the spectral information of the generated cross-polarized photon pairs is of importance for the use of such sources in applications including quantum information and communication. We demonstrate that the joint spectral intensity of the cross-polarized photon-pair source can be fully reconstructed using the quantum-classical correspondence through classical sum-frequency generation (SFG) measurements. This technique, which uses a much less complex detection system for visible light, opens the possibility of fast monitoring and control of the quantum state of (polarization-correlated) photon-pair sources to facilitate the realization of a stable and high-usability quantum source.

quant-ph↗

arXiv2020

Cardiac Segmentation with Strong Anatomical Guarantees

Convolutional neural networks (CNN) have had unprecedented success in medical imaging and, in particular, in medical image segmentation. However, despite the fact that segmentation results are closer than ever to the inter-expert variability, CNNs are not immune to producing anatomically inaccurate segmentations, even when built upon a shape prior. In this paper, we present a framework for producing cardiac image segmentation maps that are guaranteed to respect pre-defined anatomical criteria, while remaining within the inter-expert variability. The idea behind our method is to use a well-trained CNN, have it process cardiac images, identify the anatomically implausible results and warp these results toward the closest anatomically valid cardiac shape. This warping procedure is carried out with a constrained variational autoencoder (cVAE) trained to learn a representation of valid cardiac shapes through a smooth, yet constrained, latent space. With this cVAE, we can project any implausible shape into the cardiac latent space and steer it toward the closest correct shape. We tested our framework on short-axis MRI as well as apical two and four-chamber view ultrasound images, two modalities for which cardiac shapes are drastically different. With our method, CNNs can now produce results that are both within the inter-expert variability and always anatomically plausible without having to rely on a shape prior.

cs.CV↗

arXiv2020

LU-Net: a multi-task network to improve the robustness of segmentation of left ventriclular structures by deep learning in 2D echocardiography

Segmentation of cardiac structures is one of the fundamental steps to estimate volumetric indices of the heart. This step is still performed semi-automatically in clinical routine, and is thus prone to inter- and intra-observer variability. Recent studies have shown that deep learning has the potential to perform fully automatic segmentation. However, the current best solutions still suffer from a lack of robustness. In this work, we introduce an end-to-end multi-task network designed to improve the overall accuracy of cardiac segmentation while enhancing the estimation of clinical indices and reducing the number of outliers. Results obtained on a large open access dataset show that our method outperforms the current best performing deep learning solution and achieved an overall segmentation accuracy lower than the intra-observer variability for the epicardial border (i.e. on average a mean absolute error of 1.5mm and a Hausdorff distance of 5.1mm) with 11% of outliers. Moreover, we demonstrate that our method can closely reproduce the expert analysis for the end-diastolic and end-systolic left ventricular volumes, with a mean correlation of 0.96 and a mean absolute error of 7.6ml. Concerning the ejection fraction of the left ventricle, results are more contrasted with a mean correlation coefficient of 0.83 and an absolute mean error of 5.0%, producing scores that are slightly below the intra-observer margin. Based on this observation, areas for improvement are suggested.

eess.IV↗

arXiv2020

Can we describe charged nanoparticles with electrolyte theories? Insight from mesoscopic simulation techniques

Electrolyte theories enable to describe the structural and dynamical properties of simple electrolytes in solution, such as sodium chloride in water. Using these theories for aqueous solutions of charged nanoparticles is a straightforward route to extract their charge and size from experimental data. Nevertheless, for such strongly asymmetric electrolytes, the validity of the underlying approximations have never been properly challenged with exact simulation results. In the present work, well established mesoscopic numerical simulations are used to challenge the ability of advanced electrolyte theories to predict the electrical conductivity of suspensions of charged nanoparticles, in the salt-free case. The theories under investigation are based on the Debye-Fuoss-Onsager treatment of electrolyte transport. When the nanoparticles are small enough (about one nanometer large), the theoretical results agree remarkably well with the simulation ones, even in the high concentration regime (packing fraction of in nanoparticles larger than 3$\%$ ). Strikingly, for highly charged nanoparticles, the theory is able to capture the non-monotonic variation of the ratio of the electrical conductivity to its value at infinite dilution (ideal value) as a function of the concentration. However, the tested theories fail to describe the conductivity of suspensions containing larger nanoparticles ({\em e.g.} of diameter $4$~nm). Finally, only small charged nanoparticles can be considered as {\em ions}, as far as electrolyte theories are concerned.

cond-mat.soft↗

arXiv2019

Cardiac MRI Segmentation with Strong Anatomical Guarantees

Recent publications have shown that the segmentation accuracy of modern-day convolutional neural networks (CNN) applied on cardiac MRI can reach the inter-expert variability, a great achievement in this area of research. However, despite these successes, CNNs still produce anatomically inaccurate segmentations as they provide no guarantee on the anatomical plausibility of their outcome, even when using a shape prior. In this paper, we propose a cardiac MRI segmentation method which always produces anatomically plausible results. At the core of the method is an adversarial variational autoencoder (aVAE) whose latent space encodes a smooth manifold on which lies a large spectrum of valid cardiac shapes. This aVAE is used to automatically warp anatomically inaccurate cardiac shapes towards a close but correct shape. Our method can accommodate any cardiac segmentation method and convert its anatomically implausible results to plausible ones without affecting its overall geometric and clinical metrics. With our method, CNNs can now produce results that are both within the inter-expert variability and always anatomically plausible.

eess.IV↗