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Motivation High-content imaging screens provide a cost-effective and scalable way to assess cell states across diverse experimental conditions. The analysis of the acquired microscopy images involves assembling and curating raw cellular measurements into morphological profiles suitable for testing biological hypotheses. Despite being a critical step, general-purpose and adaptable tools for morphological profiling are lacking and no solution is available for the high-performance Julia programming language. Results Here, we introduce BioProfiling.jl, an efficient end-to-end solution for compiling and filtering informative morphological profiles in Julia. The package contains all the necessary data structures to curate morphological measurements and helper functions to transform, normalize and visualize profiles. Robust statistical distances and permutation tests enable quantification of the significance of the observed changes despite the high fraction of outliers inherent to high-content screens. This package also simplifies visual artifact diagnostics, thus streamlining a bottleneck of morphological analyses. We showcase the features of the package by analyzing a chemical imaging screen, in which the morphological profiles prove to be informative about the compounds' mechanisms of action and can be conveniently integrated with the network localization of molecular targets. Availability and implementation The Julia package is available on GitHub: https://github.com/menchelab/BioProfiling.jl. We also provide Jupyter notebooks reproducing our analyses: https://github.com/menchelab/BioProfilingNotebooks. The data underlying this article are available from FigShare, at https://doi.org/10.6084/m9.figshare.14784678.v2. Supplementary information Supplementary data are available at Bioinformatics online.

International audience; We provide computationally generated dataset simulating propagation of ultrasonic waves in viscous tissues in two and three dimensional domains. The dataset contains physical parameters of a human breast with a high-contrast inclusion, the acquisition setup with positions of sources and receivers, and the associated pressure-wave data at ultrasonic frequencies. We simulated the wave propagation based on seven different viscous models using the physical parameters of the breast. Furthermore, different choices of conditions for the medium's boundaries are given, namely absorbing and reflecting boundaries. The dataset allows to evaluate the performance of reconstruction methods for ultrasound imaging under attenuation model uncertainty, that is, when the precise attenuation law that characterizes the medium is unknown. In addition, the dataset enables to evaluate the robustness of inverse scheme in the context of reflecting boundary conditions where multiple reflections illuminate the sample, and/or the performance of data-processing to suppress these multiple reflections.

We construct modal outgoing Green's kernels for the simplified Galbrun's equation under spherical symmetry, in the context of helioseismology. The coefficients of the equation are C 2 functions representing the solar interior model S , complemented with an isothermal atmospheric model. We solve the equation in vectorial spherical harmonics basis to obtain modal equations for the different components of the unknown wave motions. These equations are then decoupled and written in Schrodinger form, whose coefficients are shown to be C 2 apart from at most two regular singular points, and to decay like a Coulomb potential at infinity. These properties allow us to construct an outgoing Green's kernel for each spherical mode. We also compute asymptotic expansions of coefficients up to order r − 3 as r tends to infinity, and show numerically that their accuracy is improved by including the contribution from the gravity although this term is of order r − 3 .

International audience

Mean-field games (MFGs) and the best-reply strategy (BRS) are two methods of describing competitive optimisation of systems of interacting agents. The latter can be interpreted as an approximation of the respective MFG system. In this paper, we present an analysis and comparison of the two approaches in the stationary case. We provide novel existence and uniqueness results for the stationary boundary value problems related to the MFG and BRS formulations, and we present an analytical and numerical comparison of the two paradigms in some specific modelling situations.

In this paper, we introduce and analyze an asymptotic-preserving scheme for Lotka-Volterra parabolic equations. It is a class of nonlinear and nonlocal stiff equations, which describes the evolution of a population structured with phenotypic trait. In a regime of long time and small mutations, the population concentrates at a set of dominant traits. The dynamics of this concentration is described by a constrained Hamilton-Jacobi equation, which is a system coupling a Hamilton-Jacobi equation with a Lagrange multiplier determined by a constraint. This coupling makes the equation nonlocal. Moreover, the constraint does not enjoy much regularity, since it can have jumps. The scheme we propose is convergent in all the regimes, and enjoys stability in the long time and small mutations limit. Moreover, we prove that the limiting scheme converges towards the viscosity solution of the constrained Hamilton-Jacobi equation, despite the lack of regularity of the constraint. The theoretical analysis of the schemes is illustrated and complemented with numerical simulations.

International audience; In this paper, we study the mathematical imaging problem of diffraction tomography (DT), which is an inverse scattering technique used to find material properties of an object by illuminating it with probing waves and recording the scattered waves. Conventional DT relies on the Fourier diffraction theorem, which is applicable under the condition of weak scattering. However, if the object has high contrasts or is too large compared to the wavelength, it tendsto produce multiple scattering, which complicates the reconstruction. We give a survey on diffraction tomography and compare the reconstruction of low and high contrast objects. We also implement and compare the reconstruction using the full waveform inversion method which, contrary to the Born and Rytov approximations, works with the total field and is more robust to multiple scattering.

Understanding how populations adapt to abrupt environmental change is necessary to predict responses to future challenges, but identifying specific adaptive variants, quantifying their responses to selection and reconstructing their detailed histories is challenging in natural populations. Here, we use Arabidopsis from the Cape Verde Islands as a model to investigate the mechanisms of adaptation after a sudden shift to a more arid climate. We find genome-wide evidence of adaptation after a multivariate change in selection pressures. In particular, time to flowering is reduced in parallel across islands, substantially increasing fitness. This change is mediated by convergent de novo loss of function of two core flowering time genes: FRI on one island and FLC on the other. Evolutionary reconstructions reveal a case where expansion of the new populations coincided with the emergence and proliferation of these variants, consistent with models of rapid adaptation and evolutionary rescue.

Let $p$ be a prime number and $k$ an algebraically closed field with characteristic $\ell \neq p$. We show that the supercuspidal support of irreducible smooth $k$-representations of Levi subgroups $\textrm {M}^{\prime}$ of $\textrm {SL}_n(F)$ is unique up to $\textrm {M}^{\prime}$-conjugation, where $F$ is either a finite field of characteristic $p$ or a non-Archimedean locally compact field of residual characteristic $p$.

We consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of visco-acoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is performed by an iterative minimization algorithm. Firstly, we investigate the robustness of the algorithm with respect to attenuation model uncertainty, that is, when different attenuation models are used to simulate synthetic observation data and for the inversion, respectively. Secondly, to handle data-sets with multiple reflections generated by wall boundaries around the domain, we perform inversion using complex frequencies, and show that it offers a robust framework that alleviates the difficulties of multiple reflections. To illustrate the efficiency of the algorithm, we perform numerical simulations of ultrasound imaging experiments to reconstruct a synthetic breast sample that contains an inclusion of high-contrast properties. We perform experiments in two and three dimensions, where the latter also serves to demonstrate the numerical feasibility in a large-scale configuration., Comment: 30 pages, 13 figures

International audience

We investigate the numerical computation of physical modal Green's kernels for the time-harmonic Galbrun's equation in helioseismology under spherical symmetry. These kernels are the coefficients of the 3D Green's kernels in the vector spherical harmonic expansion. In a previous work, we have characterized the physical kernels for the isothermal radial solar background model S-AtmoI and provide their well-posedness results. Here, we provide an algorithm to compute efficiently these kernels for all receiver and source positions in a region of interest and develop the technical ingredients for its implementation. The kernels are built from the solution of a scalar wave equation for the radial displacement. The solution and its derivative which are both necessary to assemble the Green's kernel are obtained by solving a first-order system using the HDG method. This approach extends previous works considering a scalar wave equation and allows to model not only the pressure modes but also the surface and internal gravity waves. While being physically more interesting, this problem raises additional numerical difficulties. In particular, the solution of the Schrodinger equation for the radial displacement is singular without attenuation and it is thus preferable to solve the original equation. Moreover, for low frequencies and high-modes, the potential switches sign in the atmosphere which requires the position of the artificial boundary to be further away from the solar surface in order to capture the correct physical solution.; Dans ce travail, nous étudions et calculons les noyaux de Green modaux pour l’équation de Galbrun pour les ondes harmoniques dans un problème d’héliosismologie avec symétrie sphérique. Ces noyaux sont les coefficients des noyaux de Green 3D décomposés en harmoniques sphériques vectorielles. Dans nos travaux précédents, nous avons caractérisé les noyaux physiques pour le milieu solaire isothermal S-AtmoI, en donnant les résultats sur le caractère bien-posé du problème. Dans ce travail, nous définissons un algorithme pour calculer de manière efficace et précise ces noyaux, pour tous les récepteurs et les sources, et développons tous les ingrédients techniques à sa mise en place. Les noyaux sont construits à partir de la solution de l’équation d’onde pour le déplacement radial. Plus précisément, la solution et sa dérivée sont toutes les deux nécessaires pour assembler les noyaux de Green et sont obtenues à partir du système du premier-ordre en utilisant la méthode de discrétisation de Galerkin discontinue hybride. Cette approche étend nos travaux précédents sur l’équation d’onde scalaire, et nous permet de modéliser non seulement les modes acoustiques du soleil, mais également les ondes de gravité de surface et internes. Ce problème vectoriel révèle aussi des difficultés numériques additionnelles. En particulier, la solution de l’équation de Schrödinger pour le déplacement radial est singulière dans le cas sans atténuation, et il est ainsi préférable de résoudre l’équation originale à la place. De plus, à fréquences basses et modes de hauts degrés, le potentiel change de signe dans l’atmosphère, ce qui implique que la condition de radiation pour la troncature du domaine numérique doit être placée bien plus loin que la surface solaire afin d’obtenir la solution correcte.

In this paper, we study the mathematical imaging problem of diffraction tomography (DT), which is an inverse scattering technique used to find material properties of an object by illuminating it with probing waves and recording the scattered waves. Conventional DT relies on the Fourier diffraction theorem, which is applicable under the condition of weak scattering. However, if the object has high contrasts or is too large compared to the wavelength, it tends to produce multiple scattering, which complicates the reconstruction. We give a survey on diffraction tomography and compare the reconstruction of low and high contrast objects. We also implement and compare the reconstruction using the full waveform inversion method which, contrary to the Born and Rytov approximations, works with the total field and is more robust to multiple scattering., 32 pages, 21 figures

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International audience; The application of the full potential of stellar seismology is made difficult by the improper modelling of the upper-most layers of solar-like stars and their influence on the modelled frequencies. Our knowledge of these so-called ‘surface effects’ has improved thanks to the use of 3D hydrodynamical simulations, however, the calculation of eigenfrequencies relies on empirical models for the description of the Lagrangian perturbation of turbulent pressure, namely: the reduced-Γ1 model (RGM) and the gas-Γ1 model (GGM). Starting from the fully compressible turbulence equations, we derived both the GGM and RGM models by using a closure to model the flux of turbulent kinetic energy. We find that both models originate from two terms: the source of turbulent pressure due to compression produced by the oscillations and the divergence of the flux of turbulent pressure. We also demonstrate that they are both compatible with the adiabatic approximation and, additionally, that they imply a number of questionable assumptions, mainly with respect to mode physics. Among other hypotheses, it is necessary to neglect the Lagrangian perturbation of the dissipation of turbulent kinetic energy into heat and the Lagrangian perturbation of buoyancy work.

The use of the full potential of stellar seismology is made difficult by the improper modeling of the upper-most layers of solar-like stars and their influence on the modeled frequencies. Our knowledge on these \emph{surface effects} has improved thanks to the use of 3D hydrodynamical simulations but the calculation of eigenfrequencies relies on empirical models for the description of the Lagrangian perturbation of turbulent pressure: the reduced-$\Gamma_1$ model (RGM) and the gas-$\Gamma_1$ model (GGM). Starting from the fully compressible turbulence equations, we derive both the GGM and RGM models using a closure to model the flux of turbulent kinetic energy. It is found that both models originate from two terms: the source of turbulent pressure due to compression produced by the oscillations and the divergence of the flux of turbulent pressure. It is also demonstrated that they are both compatible with the adiabatic approximation but also imply a number of questionable assumptions mainly regarding mode physics. Among others hypothesis, one has to neglect the Lagrangian perturbation of the dissipation of turbulent kinetic energy into heat and the Lagrangian perturbation of buoyancy work., Comment: 7 pages, 1 figure. Accepted as a Letter in Astronomy and Astrophysic

International audience; In this work, we provide an algorithm to compute efficiently and accurately the full outgoing modal Green's kernel for the scalar wave equation in local helioseismology under spherical symmetry. Due to the high computational cost of a full Green's function, current helioseismic studies rely on single-source computations. However, a more realistic modelization of the helioseismic products (cross-covariance and power spectrum) requires the full Green's kernel. In the classical approach, the Dirac source is discretized and one simulation gives the Green's function on a line. Here, we propose a two-step algorithm which, with two simulations, provides the full kernel on the domain. Moreover, our method is more accurate, as the singularity of the solution due to the Dirac source is described exactly. In addition, it is coupled with the exact Dirichlet-to-Neumann boundary condition, providing optimal accuracy in approximating the outgoing Green's kernel, which we demonstrate in our experiments. In addition, we show that high-frequency approximations of the nonlocal radiation boundary conditions can represent accurately the helioseismic products.

Interspecific crossing experiments have shown that sex chromosomes play a major role in reproductive isolation between many pairs of species. However, their ability to act as reproductive barriers, which hamper interspecific genetic exchange, has rarely been evaluated quantitatively compared to Autosomes. This genome-wide limitation of gene flow is essential for understanding the complete separation of species, and thus speciation. Here, we develop a mainland-island model of secondary contact between hybridizing species of an XY (or ZW) sexual system. We obtain theoretical predictions for the frequency of introgressed alleles, and the strength of the barrier to neutral gene flow for the two types of chromosomes carrying multiple interspecific barrier loci. Theoretical predictions are obtained for scenarios where introgressed alleles are rare. We show that the same analytical expressions apply for sex chromosomes and autosomes, but with different sex-averaged effective parameters. The specific features of sex chromosomes (hemizygosity and absence of recombination in the heterogametic sex) lead to reduced levels of introgression on the X (or Z) compared to autosomes. This effect can be enhanced by certain types of sex-biased forces, but it remains overall small (except when alleles causing incompatibilities are recessive). We discuss these predictions in the light of empirical data comprising model-based tests of introgression and cline surveys in various biological systems.

We construct C2 representations of the background quantities that characterize the interior of the Sun and its atmosphere starting from the data-points of the standard solar model S. This model is further extended considering an isothermal atmosphere, that we refer to as model AtmoI. It is not trivial to build the C2 representations of the parameters from a discrete set of values, in particular in the transition region between the end of model S and the atmosphere. This technical work is needed as a crucial building block to study theoretically and numerically the propagation of waves in the Sun, using the equations of solar oscillations (also referred to as Galbrun's equation in aeroacoustics). The constructed models are available at http://phaidra.univie.ac.at/o:1097638., 17 pages

We study the motion of a robotic arm inside a rectangular tunnel of width 2. We prove that the configuration space S of all possible positions of the robot is a CAT(0) cubical complex. Before this work, very few families of robots were known to have CAT(0) configuration spaces. This property allows us to move the arm optimally from one position to another.

In this project, we provide an algorithm to compute efficiently and accurately the full outgoing modal Green’s kernel for the scalar wave equation in local helioseismology under spherical symmetry. The cost of computing a full Green function is well-known to be expensive and has prevented its extensive usage in local helioseismology. It is however necessary in order to interpret properly the measurements. One application is the calculation of synthetic helioseismic observables such as the cross-covariance or the power spectrum. Usually, it is supposed that the observations are coming from a single height – the “solar surface” – which requires only the Green kernel at the surface of the Sun. While yielding satisfactory comparison with helioseismic data at low frequencies, more realistic observables take into account contributions from all depths. This approach requires a full Green kernel, i.e. its values at all source and receiver depths. In this work, we propose a two-step algorithm which with two simulations gives a full kernel for each harmonic mode and frequency. Our method also accounts for the singularity of the Green kernel analytically and avoids discretization with a Dirac source directly. This feature does not only help to reduce the need for mesh refinement around the source, and but also provides more accurate values of the Green’s kernel in this region. We also demonstrate numerically that using integrated simulated observables leads to a significant travel-time difference compared to using just single-depth observables. In addition, our algorithm is coupled with the exact Dirichlet-to-Neumann boundary condition, thus provides optimal accuracy in approximating the outgoing Green kernel. We also evaluate the performance of the high-frequency approximations of the nonlocal radiation boundary conditions in terms of helioseismic quantities. Until now, these comparisons were only carried out under pure Atmo assumption, and analyzed in terms of relative error of numerical solution in the atmosphere.; En héliosismologie, la fonction de Green associée à l’équation des ondes scalaire permet de représenter des observables importants tels que la corrélation croisée ou les spectres de puissance. Elle joue donc un rôle central dans l’interprétation des mesures et son calcul est crucial. Toutefois, les algorithmes de calcul existants ont des coûts de calcul encore trop élevés pour en faire une utilisation extensive en héliosismologie locale. Pour contourner cette difficulté, on suppose que les observations sont effectuées à une altitude fixe qui représente en quelque sorte une “surface solaire” et ainsi, on se contente d’utiliser la fonction de Green définie à la surface. Bien que cela donne des comparaisons satisfaisantes avec les données héliosismiques à basses fréquences, générer des observables plus réalistes demande de prendre en compte les contributions de l’intérieur du Soleil, c’est-à-dire à différentes profondeurs. Pour cela, on a besoin de la fonction de Green complète, c’est à dire, sa valeur doit être estimée pour toutes les sources et à toutes les positions de récepteurs. Dans ce travail, nous proposons un algorithme en deux étapes qui permet, à partir de seulement deux simulations, de construire le noyau de Green complet. Notre méthode prend en compte la singularité du noyau sans avoir à discrétiser la source qui est une distribution de Dirac. La méthode numérique mise en oeuvre repose sur une formulation HDG du problème écrit en supposant la symétrie sphérique du soleil. Notre algorithme est focalisé sur la partie régulière du champ d’onde et ainsi il ne nécessite pas un raffinement du maillage autour de la source tout en nous donnant des valeurs plus précises pour les récepteurs proches de la source. Nous illustrons numériquement comment l’utilisation d’intégrales pour les simulations change de façon significative le temps de trajet par rapport aux solutions à profondeur fixe.Nous effectuons des simulations pour deuxmodèles de Soleil qui sont couplés à une condition de radiation sortante utile pour tronquer l’atmosphère du Soleil et définir ainsi un domaine de calcul. Quand notre algorithme est couplé avec la condition aux limites Dirichlet-to-Neumann exacte, nous obtenons une précision optimale des quantités héliosismiques covariance et spectre de puissance. Nous comparons également la qualité des observables en considérant différentes approximations haute-fréquences de la condition de radiation non-locale, toujours pour lecalcul des mêmes quantités héliosismiques.

In this work, we consider the time-harmonic Galbrun’s equation under spherical symmetry in the context of the wave propagation in the Sun without flow and rotation, and neglecting the perturbations to the gravitational potential. The model parameters are taken from the solar model S for the interior of the Sun, and we introduce the model AtmoCAI (ideal atmospheric behavior with constant adiabatic index) to extend them into the atmosphere. This atmospheric extension is based on the model Atmo used for the scalar wave propagation where, in addition, we assume a constant adiabatic index in the atmosphere. Due to the spherical symmetry, by writing the original equation in a vector spherical harmonic basis, we obtain the ODE for the modal radial and tangential coefficients of the unknown displacements. We then construct the outgoing modal solutions, the 3D Green’s kernel, and radiation boundary conditions. The construction is justified by indicial and asymptotic analysis of the modal radial ODE. While the singular set in the presence of attenuation only consists of the origin, our analysis shows that without attenuation, there are also other singular points which, however, have positive indicial exponents. Our asymptotic analysis makes appear the correct wavenumber and the high-order terms of the oscillatory phase function, which we use to characterize outgoing solutions. The radiation boundary conditions are built for the modal radial ODE and then derived for the initial equation. We approximate them under different hypothesis and propose some formulations that are independent of the horizontal wavenumber and can thus easily be applied for 3D problems.; Dans ce travail, nous considérons l’équation harmonique de Galbrun en symétrie sphérique pour la propagation d’ondes dans le soleil, sans flot ni rotation, et en négligeant les perturbations du potentiel de gravité. Les paramètres sont extraits du modèle S pour l’intérieur du soleil, et nous introduisons un modèle AtmoCAI (comportement atmosphérique idéal avec un indice adiabatique constant) pour leur extension dans l’atmosphère solaire. Cette extension est basée sur le modèle Atmo utilisé dans le cas scalaire, que nous enrichissons en prenant l’indice adiabatique constant. De part la symétrie sphérique, en écrivant le problème dans une base harmonique sphérique vectorielle, nous obtenons l’EDO modale pour les coefficients radiaux et tangentiels du déplacement. Nous construisons les solutions sortantes modales, le noyau de Green en 3D et obtenons des conditions aux limites de radiation. La construction est motivée par l’analyse indicielle et asymptotique de l’EDO radiale modale. En présence d’atténuation, la seule singularité est á l’origine, alors que dans le cas sans atténuation, nous identifions les autres singularités qui, cependant, ont un exposant indiciel positif. Notre analyse asymptotique fait apparaître un nombre d’onde approprié et les termes d’ordres élevés de la phase, qui nous servent à caractériser les solutions sortantes. Les conditions aux limites de radiation sont construites pour l’EDO modale puis étendues au problème initial. Nous les approximons sous différentes hypothèses et proposons plusieurs approximations independantes du nombre d’onde horizontal qui peuvent être facilement utilisées pour les problèmes 3D.

SUMMARY We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter is represented using a limited number of coefficients associated with a basis of eigenvectors of a diffusion equation, following the regularization by discretization approach. We compare several choices for the diffusion coefficient in the partial differential equations, which are extracted from the field of image processing. We first investigate their efficiency for image decomposition (accuracy of the representation with respect to the number of variables). Next, we implement the method in the quantitative reconstruction procedure for seismic imaging, following the full waveform inversion method, where the difficulty resides in that the basis is defined from an initial model where none of the actual structures is known. In particular, we demonstrate that the method may be relevant for the reconstruction of media with salt-domes. We use the method in 2-D and 3-D experiments, and show that the eigenvector representation compensates for the lack of low-frequency information, it eventually serves us to extract guidelines for the implementation of the method.

In this paper, we perform non-linear minimization using the Hybridizable Discontinuous Galerkin method (HDG) for the discretization of the forward problem, and implement the adjoint-state method for the computation of the functional derivatives. Compared to continuous and discontinuous Galerkin discretizations, HDG reduces the computational cost by working with the numerical traces, hence removing the degrees of freedom that are inside the cells. It is particularly attractive for large-scale time-harmonic quantitative inverse problems which make repeated use of the forward discretization as they rely on an iterative minimization procedure. HDG is based upon two levels of linear problems: a global system to find the numerical traces, followed by local systems to construct the volume solution. This technicality requires a careful derivation of the adjoint-state method, that we address in this paper. We work with the acoustic wave equations in the frequency domain and illustrate with a three-dimensional experiment using partial reflection-data, where we further employ the features of DG-like methods to efficiently handle the topography with p-adaptivity., 24 pages, 8 figures

The determination of background velocity by full-waveform inversion (FWI) is known to be hampered by the local minima of the data misfit caused by the phase shifts associated with background perturbations. Attraction basins for the underlying optimization problems can be computed around any nominal velocity model, and they guarantee that the misfit functional has only one (global) minimum. The attraction basins are further associated with tolerable error levels representing the maximal allowed distance between the (observed) data and the simulations (i.e., the acceptable noise level). The estimates are defined a priori, and they only require the computation of (possibly many) the first- and second-order directional derivatives of the (model to synthetic) forward map. The geometry of the search direction and the frequency influence the size of the attraction basins, and the complex frequency can be used to enlarge the basins. The size of the attraction basins for the perturbation of background velocities in classic FWI (global model parameterization) and the data-space reflectivity reformulation (migration-based traveltime [MBTT]) are compared: The MBTT reformulation substantially increases the size of the attraction basins (by a factor of 4–15). Practically, this reformulation compensates for the lack of low-frequency data. Our analysis provides guidelines for a successful implementation of the MBTT reformulation.

International audience; In this paper, we study the time-harmonic scalar equation describing the propagation of acoustic waves in the Sun's atmosphere under ideal atmospheric assumptions. We use the Liouville change of unknown to conjugate the original problem to a Schrödinger equation with a Coulomb-type potential. This transformation makes appear a new wavenumber, k, and the link with the Whittaker's equation. We consider two different problems: in the first one, with the ideal atmospheric assumptions extended to the whole space, we construct explicitly the Schwartz kernel of the resolvent, starting from a solution given by Hostler and Pratt in punctured domains, and use this to construct outgoing solutions and radiation conditions. In the second problem, we construct exact Dirichlet-to-Neumann map using Whittaker functions, and new radiation boundary conditions (RBC), using gauge functions in terms of k. The new approach gives rise to simpler RBC for the same precision compared to existing ones. The robustness of our new RBC is corroborated by numerical experiments.

Quantitative imaging of sub-surface Earth's properties in elastic media is performed from Distributed Acoustic Sensing data. A new misfit functional based upon the reciprocity-gap is designed, taking cross-correlations of displacement and strain, and these products further associate an observation with a simulation. In comparison with other misfit functionals, this one has the advantage to only require little a-priori information on the exciting sources. In particular, the misfit criterion enables the use of data from regional earthquakes (teleseismic events can be included as well), followed by exploration data to perform a multi-resolution reconstruction. The data from regional earthquakes contain the low-frequency content which is missing in the exploration ones, allowing for the recovery of the long spatial wavelength, even with very few sources. These data are used to build prior models for the subsequent reconstruction from the higher-frequency exploration data. This gives the elastic Full Reciprocity-gap Waveform Inversion method, and we demonstrate its performance with a pilot experiment for elastic isotropic reconstruction., Comment: 21 pages, 6 figures

International audience; The quantitative reconstruction of subsurface earth properties from the propagation of waves follows an iterative minimization of a misfit functional. In marine seismic exploration, the observed data usually consist of measurements of the pressure field, but dual-sensor devices also provide the normal velocity. Consequently, a reciprocity-based misfit functional is specifically designed, and it defines the full reciprocity-gap waveform inversion (FRgWI) method. This misfit functional provides additional features compared to the more traditional least-squares approaches, in particular, in that the observational and computational acquisitions can be different. Therefore, the positions and wavelets of the sources from which the measurements are acquired are not needed in the reconstruction procedure and, in fact, the numerical acquisition (for the simulations) can be chosen arbitrarily. Based on 3D experiments, FRgWI is shown to behave better than full-waveform inversion in the same context. It allows for arbitrary numerical acquisitions in two ways: when few measurements are given, a dense numerical acquisition (compared to the observational one) can be used to compensate. However, with a dense observational acquisition, a sparse computational one is shown to be sufficient, for instance, with multiple-point sources, hence reducing the numerical cost. FRgWI displays accurate reconstructions in both situations and appears more robust with respect to crosstalk than least-squares shot stacking.

In this article we investigate the phase transition phenomena that occur in a model of self-organisation through body-attitude coordination. Here, the body attitude of an agent is modelled by a rotation matrix in $${\mathbb {R}}^3$$ R 3 as in Degond et al. (Math Models Methods Appl Sci 27(6):1005–1049, 2017). The starting point of this study is a BGK equation modelling the evolution of the distribution function of the system at a kinetic level. The main novelty of this work is to show that in the spatially homogeneous case, self-organisation may appear or not depending on the local density of agents involved. We first exhibit a connection between body-orientation models and models of nematic alignment of polymers in higher-dimensional space from which we deduce the complete description of the possible equilibria. Then, thanks to a gradient-flow structure specific to this BGK model, we are able to prove the stability and the convergence towards the equilibria in the different regimes. We then derive the macroscopic models associated with the stable equilibria in the spirit of Degond et al. (Arch Ration Mech Anal 216(1):63–115, 2015, Math Models Methods Appl Sci 27(6):1005–1049, 2017).

International audience

International audience; The study of model organisms on islands may shed light on rare long-range dispersal events, uncover signatures of local evolutionary processes, and inform demographic inference on the mainland. Here, we sequenced the genomes of Arabidopsis thaliana samples from the oceanic island of Madeira. These samples include the most diverged worldwide, likely a result of long isolation on the island. We infer that colonization of Madeira happened between 70 and 85 ka, consistent with a propagule dispersalmodel (of size >= 10), or with an ecological window of opportunity. This represents a clear example of a natural long-range dispersal event in A. thaliana. Long-term effective population size on the island, rather than the founder effect, had the greatest impact on levels of diversity, and rates of coalescence. Our results uncover a selective sweep signature on the ancestral haplotype of a known translocation in Eurasia, as well as the possible importance of the low phosphorous availability in volcanic soils, and altitude, in shaping early adaptations to the island conditions. Madeiran genomes, sheltered from the complexities of continental demography, help illuminate ancient demographic events in Eurasia. Our data support a model in which two separate lineages of A. thaliana, one originating in Africa and the other from the Caucasus expanded and met in Iberia, resulting in a secondary contact zone there. Although previous studies inferred that the westward expansion of A. thaliana coincided with the spread of human agriculture, our results suggest that it happened much earlier (20-40 ka).

Sarason's Toeplitz product problem asks when the operator T u T v ‾ is bounded on various Hilbert spaces of analytic functions, where u and v are analytic. The problem is highly nontrivial for Toeplitz operators on the Hardy space and the Bergman space (even in the case of the unit disk). In this paper, we provide a complete solution to the problem for a class of Fock spaces on the complex plane. In particular, this generalizes an earlier result of Cho, Park, and Zhu.

International audience; The goal of these lecture notes is to present in a unified way various models for the dynamics of aligning self-propelled rigid bodies at different scales and the links between them. The models and methods are inspired from [12,13], but, in addition, we introduce a new model and apply on it the same methods. While the new model has its own interest, our aim is also to emphasize the methods by demonstrating their adaptability and by presenting them in a unified and simplified way. Furthermore, from the various microscopic models we derive the same macroscopic model, which is a good indicator of its universality.

We consider a multi-dimensional scalar wave equation with memory corresponding to the viscoelastic material described by a generalized Zener model. We deduce that this relaxation system is an example of a non-strictly hyperbolic system satisfying Majda's block structure condition. Well-posedness of the associated Cauchy problem is established by showing that the symbol of the spatial derivatives is uniformly diagonalizable with real eigenvalues. A long-time stability result is obtained by plane-wave analysis when the memory term allows for dissipation of energy.

International audience; We develop a variational integrator for the shallow-water equations on a rotating sphere. The variational integrator is built around a discretization of the continuous Euler-Poincar\'{e} reduction framework for Eulerian hydrodynamics. We describe the discretization of the continuous Euler-Poincar\'{e} equations on arbitrary simplicial meshes. Standard numerical tests are carried out to verify the accuracy and the excellent conservational properties of the discrete variational integrator.

The abstract is available here: https://uscholar.univie.ac.at/o:1604264

In this paper, we count factorizations of Coxeter elements in well-generated complex reflection groups into products of reflections. We obtain a simple product formula for the exponential generating function of such factorizations, which is expressed uniformly in terms of natural parameters of the group. In the case of factorizations of minimal length, we recover a formula due to P. Deligne, J. Tits and D. Zagier in the real case and to D. Bessis in the complex case. For the symmetric group, our formula specializes to a formula of D. M. Jackson., Comment: 38 pages, including 18 pages appendix. To appear in Journal of the London Mathematical Society. v3: minor changes and corrected references; v2: added extended discussion on the definition of Coxeter elements

International audience; In this paper we study balanced growth path solutions of a Boltzmann mean field game model proposed by Lucas et al [13] to model knowledge growth in an economy. Agents can either increase their knowledge level by exchanging ideas in learning events or by producing goods with the knowledge they already have. The existence of balanced growth path solutions implies exponential growth of the overall production in time. We proof existence of balanced growth path solutions if the initial distribution of individuals with respect to their knowledge level satisfies a Pareto-tail condition. Furthermore we give first insights into the existence of such solutions if in addition to production and knowledge exchange the knowledge level evolves by geometric Brownian motion.

In this paper we analyze a Boltzmann type mean field game model for knowledge growth, which was proposed by Lucas and Moll. We discuss the underlying mathematical model, which consists of a coupled system of a Boltzmann type equation for the agent density and a Hamilton-Jacobi-Bellman equation for the optimal strategy. We study the analytic features of each equation separately and show local in time existence and uniqueness for the fully coupled system. Furthermore we focus on the construction and existence of special solutions, which relate to exponential growth in time - so called balanced growth path solutions. Finally we illustrate the behavior of solutions for the full system and the balanced growth path equations with numerical simulations., Comment: 6 figures

Adaptation lies at the heart of Darwinian evolution. Accordingly, numerous studies have tried to provide a formal framework for the description of the adaptive process. Of these, two complementary modeling approaches have emerged: While so-called adaptive-walk models consider adaptation from the successive fixation of de novo mutations only, quantitative genetic models assume that adaptation proceeds exclusively from preexisting standing genetic variation. The latter approach, however, has focused on short-term evolution of population means and variances rather than on the statistical properties of adaptive substitutions. Our aim is to combine these two approaches by describing the ecological and genetic factors that determine the genetic basis of adaptation from standing genetic variation in terms of the effect-size distribution of individual alleles. Specifically, we consider the evolution of a quantitative trait to a gradually changing environment. By means of analytical approximations, we derive the distribution of adaptive substitutions from standing genetic variation, that is, the distribution of the phenotypic effects of those alleles from the standing variation that become fixed during adaptation. Our results are checked against individual-based simulations. We find that, compared to adaptation from de novo mutations, (i) adaptation from standing variation proceeds by the fixation of more alleles of small effect and (ii) populations that adapt from standing genetic variation can traverse larger distances in phenotype space and, thus, have a higher potential for adaptation if the rate of environmental change is fast rather than slow.

Fully Packed Loop configurations in a triangle (TFPLs) first appeared in the study of ordinary Fully Packed Loop configurations (FPLs) on the square grid where they were used to show that the number of FPLs with a given link pattern that has m nested arches is a polynomial function in m. It soon turned out that TFPLs possess a number of other nice properties. For instance, they can be seen as a generalized model of Littlewood-Richardson coefficients. We start our article by introducing oriented versions of TFPLs; their main advantage in comparison with ordinary TFPLs is that they involve only local constraints. Three main contributions are provided. Firstly, we show that the number of ordinary TFPLs can be extracted from a weighted enumeration of oriented TFPLs and thus it suffices to consider the latter. Secondly, we decompose oriented TFPLs into two matchings and use a classical bijection to obtain two families of nonintersecting lattice paths (path tangles). This point of view turns out to be extremely useful for giving easy proofs of previously known conditions on the boundary of TFPLs necessary for them to exist. One example is the inequality d(u)+d(v), 40 pages, 31 figures

International audience; We present an introduction to the orbital stability of relative equilibria of Hamiltonian dynamical systems on (finite and infinite dimensional) Banach spaces. A convenient formulation of the theory of Hamiltonian dynamics with symmetry and the corresponding momentum maps is proposed that allows us to highlight the interplay between (symplectic) geometry and (functional) analysis in the proofs of orbital stability of relative equilibria via the so-called energy-momentum method. The theory is illustrated with examples from finite dimensional systems, as well as from Hamiltonian PDE's, such as solitons, standing and plane waves for the nonlinear Schrödinger equation, for the wave equation, and for the Manakov system.

International audience; Fisher's geometric model has been widely used to study the effects of pleiotropy and organismic complexity on phenotypic adaptation. Here, we study a version of Fisher's model in which a population adapts to a gradually moving optimum. Key parameters are the rate of environmental change, the dimensionality of phenotype space, and the patterns of mutational and selectional correlations. We focus on the distribution of adaptive substitutions, that is, the multivariate distribution of the phenotypic effects of fixed beneficial mutations. Our main results are based on an "adaptive-walk approximation," which is checked against individual-based simulations. We find that (1) the distribution of adaptive substitutions is strongly affected by the ecological dynamics and largely depends on a single composite parameter γ, which scales the rate of environmental change by the "adaptive potential" of the population; (2) the distribution of adaptive substitution reflects the shape of the fitness landscape if the environment changes slowly, whereas it mirrors the distribution of new mutations if the environment changes fast; (3) in contrast to classical models of adaptation assuming a constant optimum, with a moving optimum, more complex organisms evolve via larger adaptive steps.

International audience; An increasing number of studies demonstrate phenotypic and genetic changes in natural populations that are subject to climate change, and there is hope that some of these changes will contribute to avoiding species extinctions ('evolutionary rescue'). Here, we review theoretical models of rapid evolution in quantitative traits that can shed light on the potential for adaptation to a changing climate. Our focus is on quantitative-genetic models with selection for a moving phenotypic optimum. We point out that there is no one-to-one relationship between the rate of adaptation and population survival, because the former depends on relative fitness and the latter on absolute fitness. Nevertheless, previous estimates that sustainable rates of genetically based change usually do not exceed 0.1 haldanes (i.e., phenotypic standard deviations per generation) are probably correct. Survival can be greatly facilitated by phenotypic plasticity, and heritable variation in plasticity can further speed up genetic evolution. Multivariate selection and genetic correlations are frequently assumed to constrain adaptation, but this is not necessarily the case and depends on the geometric relationship between the fitness landscape and the structure of genetic variation. Similar conclusions hold for adaptation to shifting spatial gradients. Recent models of adaptation in multispecies communities indicate that the potential for rapid evolution is strongly influenced by interspecific competition.

International audience; Mutation may impose a substantial load on populations, which varies according to the reproductive mode of organisms. Over the past years, various authors used adaptive landscape models to predict the long-term effect of mutation on mean fitness; however, many of these studies assumed very weak mutation rates, so that at most one mutation segregates in the population. In this article, we derive several simple approximations (confirmed by simulations) for the mutation load at high mutation rate (U), using a general model that allows us to play with the number of selected traits (n), the degree of pleiotropy of mutations, and the shape of the fitness function (which affects the average sign and magnitude of epistasis among mutations). When mutations have strong fitness effects, the equilibrium fitness inline image of sexuals and asexuals is close to inline image; under weaker mutational effects, sexuals reach a different regime where inline image is a simple function of U and of a parameter describing the shape of the fitness function. Contrarily to weak mutation results showing that inline image is an increasing function of population size and a decreasing function of n, these parameters may have opposite effects in sexual populations at high mutation rate.

In this work we introduce and study tree-like tableaux, which are certain fillings of Ferrers diagrams in simple bijection with permutation tableaux and alternative tableaux. We exhibit an elementary insertion procedure on our tableaux which gives a clear proof that tableaux of size n are counted by n!, and which moreover respects most of the well-known statistics studied originally on alternative and permutation tableaux. Our insertion procedure allows to define in particular two simple new bijections between tree-like tableaux and permutations: the first one is conceived specifically to respect the generalized pattern 2-31, while the second one respects the underlying tree of a tree-like tableau., Dans ce travail nous introduisons et étudions les tableaux boisés, qui sont certains remplissages de diagrammes de Ferrers en bijection simple avec les tableaux de permutation et les tableaux alternatifs. Nous décrivons une procédure d'insertion élémentaire sur nos tableaux qui donne une preuve limpide que les tableaux de taille n sont comptés par n!, et qui de plus respecte la plupart des statistiques standard sur les tableaux de permutation et tableaux alternatifs. Notre procédure d'insertion permet en particulier de définir deux nouvelles bijections simples entre tableaux et permutations: la première est conçue spécifiquement pour respecter le motif généralisé 2-31 sur les permutations, tandis que la deuxième respecte l'arbre binaire sous-jacent à un tableau boisé.