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Causal inference methods based on conditional independence construct Markov equivalent graphs, and cannot be applied to bivariate cases. The approaches based on independence of cause and mechanism state, on the contrary, that causal discovery can be inferred for two observations. In our contribution, we challenge to reconcile these two research directions. We study the role of latent variables such as latent instrumental variables and hidden common causes in the causal graphical structures. We show that the methods based on the independence of cause and mechanism, indirectly contain traces of the existence of the hidden instrumental variables. We derive a novel algorithm to infer causal relationships between two variables, and we validate the proposed method on simulated data and on a benchmark of cause-effect pairs. We illustrate by our experiments that the proposed approach is simple and extremely competitive in terms of empirical accuracy compared to the state-of-the-art methods.

In this paper, we prove the Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture for unitary groups $U_n\times U_{n+1}$ in all the endoscopic cases. Our main technical innovation is the computation of the contributions of certain cuspidal data, called $*$-generic, to the Jacquet-Rallis trace formula for linear groups. We offer two different computations of these contributions: one, based on truncation, is expressed in terms of regularized Rankin-Selberg periods of Eisenstein series and Flicker-Rallis intertwining periods. The other, built upon Zeta integrals, is expressed in terms of functionals on the Whittaker model. A direct proof of the equality between the two expressions is also given. Finally several useful auxiliary results about the spectral expansion of the Jacquet-Rallis trace formula are provided., Comment: In English

The objective of this study is to highlight the effect of porosity variation in a topology optimization process in the field of fluid dynamics. Usually a penalization term added to momentum equation provides to get material distribution. Every time material is added inside the computational domain, there is creation of new fluid-solid interfaces and apparition of gradient of porosity. However, at present, porosity variation is not taken account in topology optimization and the penalization term used to locate the solid is analogous to a Darcy term used for flows in porous media. With that in mind, in this paper, we first develop an original one-domain macroscopic model for the modelling of flow through spatially varying porous media that goes beyond the scope of Darcy regime. Next, we numerically solve a topology optimization problem and compare the results obtained with the standard model that does not include effect of porosity variation with those obtained with our model. Among our results, we show for instance that the designs obtained are different but percentages of reduction of objective functional remain quite close (below 4\% of difference). In addition, we illustrate effects of porosity and particle diameter values on final optimized designs.

Frequency-domain full-waveform inversion (FWI) is suitable for long-offset stationary-recording acquisition, since reliable subsurface models can be reconstructed with a few frequencies and attenuation is easily implemented without computational overhead. In the frequency domain, wave modeling is a Helmholtz-type boundary-value problem which requires to solve a large and sparse system of linear equations per frequency with multiple right-hand sides (sources). This system can be solved with direct or iterative methods. While the former are suitable for FWI application on 3D dense OBC acquisitions covering spatial domains of moderate size, the later should be the approach of choice for sparse node acquisitions covering large domains (more than 50 millions of unknowns). Fast convergence of iterative solvers for Helmholtz problems remains however challenging in high frequency regime due to the non definiteness of the Helmholtz operator, on one side and on the discretization constraints in order to minimize the dispersion error for a given frequency, on the other side, hence requiring efficient preconditioners. In this study, we use the Krylov subspace GMRES iterative solver combined with a two-level domain-decomposition preconditioner. Discretization relies on continuous Lagrange finite elements of order 3 on unstructured tetrahedral meshes to comply with complex geometries and adapt the size of the elements to the local wavelength ($h$-adaptivity). We assess the accuracy, the convergence and the scalability of our method with the acoustic 3D SEG/EAGE Overthrust model up to a frequency of 20~Hz., Comment: arXiv admin note: substantial text overlap with arXiv:2004.06309

Frequency-domain full-waveform inversion (FWI) is suitable for long-offset stationary-recording acquisition, since reliable subsurface models can be reconstructed with a few frequencies and attenuation is easily implemented without computational overhead. In the frequency domain, wave modelling is a Helmholtz-type boundary-value problem which requires to solve a large and sparse system of linear equations per frequency with multiple right-hand sides (sources). This system can be solved with direct or iterative methods. While the former are suitable for FWI application on 3D dense OBC acquisitions covering spatial domains of moderate size, the later should be the approach of choice for sparse node acquisitions covering large domains (more than 50 millions of unknowns). Fast convergence of iterative solvers for Helmholtz problems remains however challenging due to the non definiteness of the Helmholtz operator, hence requiring efficient preconditioners. In this study, we use the Krylov subspace GMRES iterative solver combined with a multi-level domain-decomposition preconditioner. Discretization relies on continuous finite elements on unstructured tetrahedral meshes to comply with complex geometries and adapt the size of the elements to the local wavelength ($h$-adaptivity). We assess the convergence and the scalability of our method with the acoustic 3D SEG/EAGE Overthrust model up to a frequency of 20~Hz and discuss its efficiency for multi right-hand side processing.

This paper deals with bathymetry-oriented optimization in the case of long waves with small amplitude. Under these two assumptions, the free-surface incompressible Navier-Stokes system can be written as a wave equation where the bathymetry appears as a parameter in the spatial operator. Looking then for time-harmonic fields and writing the bottom topography as a perturbation of a flat bottom, we end up with a heterogeneous Helmholtz equation with impedance boundary condition. In this way, we study some PDE-constrained optimization problem for a Helmholtz equation in heterogeneous media whose coefficients are only bounded with bounded variation. We provide necessary condition for a general cost function to have at least one optimal solution. We also prove the convergence of a finite element approximation of the solution to the considered Helmholtz equation as well as the convergence of discrete optimum toward the continuous ones. We end this paper with some numerical experiments to illustrate the theoretical results and show that some of their assumptions could actually be removed.

We analyze the convergence of the one-level overlapping domain decomposition preconditioner SORAS (Symmetrized Optimized Restricted Additive Schwarz) applied to a generic linear system whose matrix is not necessarily symmetric/self-adjoint nor positive definite. By generalizing the theory for the Helmholtz equation developed in [I.G. Graham, E.A. Spence, and J. Zou, SIAM J.Numer.Anal., 2020], we identify a list of assumptions and estimates that are sufficient to obtain an upper bound on the norm of the preconditioned matrix, and a lower bound on the distance of its field of values from the origin. We stress that our theory is general in the sense that it is not specific to one particular boundary value problem. Moreover, it does not rely on a coarse mesh whose elements are sufficiently small. As an illustration of this framework, we prove new estimates for overlapping domain decomposition methods with Robin-type transmission conditions for the heterogeneous reaction-convection-diffusion equation (to prove the stability assumption for this equation we consider the case of a coercive bilinear form, which is non-symmetric, though).

We compute the quantum tunneling rate of dilute axion stars close to the maximum mass [P.H. Chavanis, Phys. Rev. D {\bf 84}, 043531 (2011)] using the theory of instantons. We confirm that the lifetime of metastable states is extremely long, scaling as $t_{\rm life}\sim e^N\, t_D$ (except close to the critical point), where $N$ is the number of axions in the system and $t_D$ is the dynamical time ($N\sim 10^{57}$ and $t_D\sim 10\, {\rm hrs}$ for typical QCD axion stars; $N\sim 10^{96}$ and $t_D\sim 100\, {\rm Myrs}$ for the quantum core of a dark matter halo made of ultralight axions). Therefore, metastable equilibrium states can be considered as stable equilibrium states in practice. We develop a finite size scaling theory close to the maximum mass and predict that the collapse time at criticality scales as $t_{\rm coll}\sim N^{1/5}t_D$ instead of being infinite as when fluctuations are neglected. The collapse time is smaller than the age of the universe for QCD axion stars and larger than the age of the universe for dark matter cores made of ultralight axions. We also consider the thermal tunneling rate and reach the same conclusions. We compare our results with similar results obtained for Bose-Einstein condensates in laboratory, globular clusters in astrophysics, and quantum field theory in the early Universe.

Mammography is the primary imaging modality used for early detection and diagnosis of breast cancer. X-ray mammogram analysis mainly refers to the localization of suspicious regions of interest followed by segmentation, towards further lesion classification into benign versus malignant. Among diverse types of breast abnormalities, masses are the most important clinical findings of breast carcinomas. However, manually segmenting breast masses from native mammograms is time-consuming and error-prone. Therefore, an integrated computer-aided diagnosis system is required to assist clinicians for automatic and precise breast mass delineation. In this work, we present a two-stage multi-scale pipeline that provides accurate mass contours from high-resolution full mammograms. First, we propose an extended deep detector integrating a multi-scale fusion strategy for automated mass localization. Second, a convolutional encoder-decoder network using nested and dense skip connections is employed to fine-delineate candidate masses. Unlike most previous studies based on segmentation from regions, our framework handles mass segmentation from native full mammograms without any user intervention. Trained on INbreast and DDSM-CBIS public datasets, the pipeline achieves an overall average Dice of 80.44% on INbreast test images, outperforming state-of-the-art. Our system shows promising accuracy as an automatic full-image mass segmentation system. Extensive experiments reveals robustness against the diversity of size, shape and appearance of breast masses, towards better interaction-free computer-aided diagnosis.

Objective : Abdominal anatomy segmentation is crucial for numerous applications from computer-assisted diagnosis to image-guided surgery. In this context, we address fully-automated multi-organ segmentation from abdominal CT and MR images using deep learning. Methods: The proposed model extends standard conditional generative adversarial networks. Additionally to the discriminator which enforces the model to create realistic organ delineations, it embeds cascaded partially pre-trained convolutional encoder-decoders as generator. Encoder fine-tuning from a large amount of non-medical images alleviates data scarcity limitations. The network is trained end-to-end to benefit from simultaneous multi-level segmentation refinements using auto-context. Results : Employed for healthy liver, kidneys and spleen segmentation, our pipeline provides promising results by outperforming state-of-the-art encoder-decoder schemes. Followed for the Combined Healthy Abdominal Organ Segmentation (CHAOS) challenge organized in conjunction with the IEEE International Symposium on Biomedical Imaging 2019, it gave us the first rank for three competition categories: liver CT, liver MR and multi-organ MR segmentation. Conclusion : Combining cascaded convolutional and adversarial networks strengthens the ability of deep learning pipelines to automatically delineate multiple abdominal organs, with good generalization capability. Significance : The comprehensive evaluation provided suggests that better guidance could be achieved to help clinicians in abdominal image interpretation and clinical decision making.

Segmentation of abdominal organs has been a comprehensive, yet unresolved, research field for many years. In the last decade, intensive developments in deep learning (DL) have introduced new state-of-the-art segmentation systems. In order to expand the knowledge on these topics, the CHAOS - Combined (CT-MR) Healthy Abdominal Organ Segmentation challenge has been organized in conjunction with IEEE International Symposium on Biomedical Imaging (ISBI), 2019, in Venice, Italy. CHAOS provides both abdominal CT and MR data from healthy subjects for single and multiple abdominal organ segmentation. Five different but complementary tasks have been designed to analyze the capabilities of current approaches from multiple perspectives. The results are investigated thoroughly, compared with manual annotations and interactive methods. The analysis shows that the performance of DL models for single modality (CT / MR) can show reliable volumetric analysis performance (DICE: 0.98 $\pm$ 0.00 / 0.95 $\pm$ 0.01) but the best MSSD performance remain limited (21.89 $\pm$ 13.94 / 20.85 $\pm$ 10.63 mm). The performances of participating models decrease significantly for cross-modality tasks for the liver (DICE: 0.88 $\pm$ 0.15 MSSD: 36.33 $\pm$ 21.97 mm) and all organs (DICE: 0.85 $\pm$ 0.21 MSSD: 33.17 $\pm$ 38.93 mm). Despite contrary examples on different applications, multi-tasking DL models designed to segment all organs seem to perform worse compared to organ-specific ones (performance drop around 5\%). Besides, such directions of further research for cross-modality segmentation would significantly support real-world clinical applications. Moreover, having more than 1500 participants, another important contribution of the paper is the analysis on shortcomings of challenge organizations such as the effects of multiple submissions and peeking phenomena., Comment: 23 pages, 11 tables, 9 figures

Bose-Einstein Condensate Dark Matter (BECDM; also known as Fuzzy Dark Matter) is motivated by fundamental physics and has recently received significant attention as a serious alternative to the established Cold Dark Matter (CDM) model. We perform cosmological simulations of BECDM gravitationally coupled to baryons and investigate structure formation at high redshifts ($z \gtrsim 5$) for a boson mass $m=2.5\cdot 10^{-22}~{\rm eV}$, exploring the dynamical effects of its wavelike nature on the cosmic web and the formation of first galaxies. Our BECDM simulations are directly compared to CDM as well as to simulations where the dynamical quantum potential is ignored and only the initial suppression of the power spectrum is considered -- a Warm Dark Matter-like ("WDM") model often used as a proxy for BECDM. Our simulations confirm that "WDM" is a good approximation to BECDM on large cosmological scales even in the presence of the baryonic feedback. Similarities also exist on small scales, with primordial star formation happening both in isolated haloes and continuously along cosmic filaments; the latter effect is not present in CDM. Global star formation and metal enrichment in these first galaxies are delayed in BECDM/"WDM" compared to the CDM case: in BECDM/"WDM" first stars form at $z\sim 13$/$13.5$ while in CDM star formation starts at $z\sim 35$. The signature of BECDM interference, not present in "WDM", is seen in the evolved dark matter power spectrum: although the small scale structure is initially suppressed, power on kpc scales is added at lower redshifts. Our simulations lay the groundwork for realistic simulations of galaxy formation in BECDM., Comment: 19 pages, 12 figures, submitted to MNRAS

We study the core mass -- halo mass relation of bosonic dark matter halos, in the form of self-gravitating Bose-Einstein condensates, harbouring a supermassive black hole. We use the ``velocity dispersion tracing'' relation according to which the velocity dispersion in the core $v_c^2\sim GM_c/R_c$ is of the same order as the velocity dispersion in the halo $v_h^2\sim GM_h/r_h$ (this relation can be justified from thermodynamical arguments) and the approximate analytical mass-radius relation of the quantum core in the presence of a central black hole obtained in our previous paper [P.H. Chavanis, Eur. Phys. J. Plus 134, 352 (2019)]. For a given minimum halo mass $(M_h)_{\rm min}\sim 10^8\, M_{\odot}$ determined by the observations, the only free parameter of our model is the scattering length $a_s$ of the bosons (their mass $m$ is then determined by the characteristics of the minimum halo). For noninteracting bosons and for bosons with a repulsive self-interaction, we find that the core mass $M_c$ increases with the halo mass $M_h$ and achieves a maximum value $(M_c)_{\rm max}$ at some halo mass $(M_h)_{*}$ before decreasing. The whole series of equilibria is stable. For bosons with an attractive self-interaction, we find that the core mass achieves a maximum value $(M_c)_{\rm max}$ at some halo mass $(M_h)_{*}$ before decreasing. The series of equilibria becomes unstable above a maximum halo mass $(M_h)_{\rm max}\ge (M_h)_{*}$. In the absence of black hole $(M_h)_{\rm max}=(M_h)_{*}$. At that point, the quantum core (similar to a dilute axion star) collapses. We perform a similar study for fermionic dark matter halos. We find that they behave similarly to bosonic dark matter halos with a repulsive self-interaction, the Pauli principle for fermions playing the role of the repulsive self-interaction for bosons.

We introduce an adaptive element-based domain decomposition (DD) method for solving saddle point problems defined as a block two by two matrix. The algorithm does not require any knowledge of the constrained space. We assume that all sub matrices are sparse and that the diagonal blocks are spectrally equivalent to a sum of positive semi definite matrices. The latter assumption enables the design of adaptive coarse space for DD methods that extends the GenEO theory to saddle point problems. Numerical results on three dimensional elasticity problems for steel-rubber structures discretized by a finite element with continuous pressure are shown for up to one billion degrees of freedom.

This paper proposes an automatic method for scapula bone segmentation from Magnetic Resonance (MR) images using deep learning. The purpose of this work is to incorporate anatomical priors into a conditional adversarial framework, given a limited amount of heterogeneous annotated images. Our approach encourages the segmentation model to follow the global anatomical properties of the underlying anatomy through a learnt non-linear shape representation while the adversarial contribution refines the model by promoting realistic delineations. These contributions are evaluated on a dataset of 15 pediatric shoulder examinations, and compared to state-of-the-art architectures including UNet and recent derivatives. The significant improvements achieved bring new perspectives for the pre-operative management of musculo-skeletal diseases.

In hierarchical models of structure formation, the first galaxies form in low-mass dark matter potential wells, probing the behavior of dark matter on kiloparsec (kpc) scales. Even though these objects are below the detection threshold of current telescopes, future missions will open an observational window into this emergent world. In this Letter we investigate how the first galaxies are assembled in a `fuzzy' dark matter (FDM) cosmology where dark matter is an ultralight $\sim 10^{-22}$~eV boson and the primordial stars are expected to form along dense dark matter filaments. Using a first-of-its-kind cosmological hydrodynamical simulation, we explore the interplay between baryonic physics and unique wavelike features inherent to FDM. In our simulation, the dark matter filaments show coherent interference patterns on the boson de Broglie scale and develop cylindrical soliton-like cores which are unstable under gravity and collapse into kpc-scale spherical solitons. Features of the dark matter distribution are largely unaffected by the baryonic feedback. On the contrary, the distributions of gas and stars, which do form along the entire filament, exhibit central cores imprinted by dark matter -- a smoking gun signature of FDM., Comment: 6 pages, 2 figures, accepted to Phys. Rev. Lett

We determine the mass-radius relation of self-gravitating Bose-Einstein condensates with an attractive $-1/r$ external potential created by a central mass. Following our previous work [P.H. Chavanis, Phys. Rev. D 84, 043531 (2011)], we use an analytical approach based on a Gaussian ansatz. We consider the case of noninteracting bosons as well as the case of self-interacting bosons with a repulsive or an attractive self-interaction. These results may find application in the context of dark matter halos made of self-gravitating Bose-Einstein condensates. In that case, the central mass may mimic a supermassive black hole. We apply our results to ultralight axions with an attractive self-interaction. We determine how the central black hole affects the mass-radius relation and the maximum mass of axionic halos found in our previous papers. Our approximate analytical results based on the Gaussian ansatz are compared with exact analytical results obtained in particular limits.

The present understanding of supernova explosion of massive stars as a two-step process, with an initial gravitational collapse toward the center of the star followed by an expansion of matter after a bouncing on the core, meets several difficulties. We show that it is not the only possible one: a simple model based on fluid mechanics, catastrophe theory, and stability properties of the equilibrium state shows that one can have also a simultaneous inward/outward motion in the early stage of the instability of the supernova described by a dynamical saddle-center bifurcation. The existence of this simultaneous inward/outward motion is sensitive to the model in such systems with long-range interactions. If a constant temperature is assumed (canonical ensemble), an overall inward motion occurs, but if one imposes with the same equation of state the constraint of energy conservation (microcanonical ensemble) there is an inward velocity field near the center of the star together with an outward velocity field in the rest of the star. We discuss the expansion stage of the remnants away from the collapsed core, and propose a new explanation for the formation of shock waves in the ejecta which differs from the usual Sedov-Taylor self-similar description.

Supernovae explosions of massive stars are nowadays believed to result from a two-step process, with an initial gravitational core collapse followed by an expansion of matter after a bouncing on the core. This scenario meets several difficulties. We show that it is not the only possible one: a simple model based on fluid mechanics and stability properties of the equilibrium state shows that one can have also a simultaneous inward/outward motion in the early stage of the instability of the supernova. This shows up in the slow sweeping across a saddle-center bifurcation found when considering equilibrium states associated to the constraint of energy conservation. We first discuss the weakly nonlinear regime in terms of a Painlev\'e I equation. We then show that the strongly nonlinear regime displays a self-similar behavior of the core collapse. Finally, the expansion of the remnants is revisited as an isentropic process leading to shocks formation., Comment: arXiv admin note: substantial text overlap with arXiv:1909.03474

We develop a general formalism to determine the statistical equilibrium states of self-gravitating systems in general relativity and complete previous works on the subject. Our results are valid for an arbitrary form of entropy but, for illustration, we explicitly consider the Fermi-Dirac entropy for fermions. The maximization of entropy at fixed mass-energy and particle number determines the distribution function of the system and its equation of state. It also implies the Tolman-Oppenheimer-Volkoff equations of hydrostatic equilibrium and the Tolman-Klein relations. Our paper provides all the necessary equations that are needed to construct the caloric curves of self-gravitating fermions in general relativity as done in recent works. We consider the nonrelativistic limit $c\rightarrow +\infty$ and recover the equations obtained within the framework of Newtonian gravity. We also discuss the inequivalence of statistical ensembles as well as the relation between the dynamical and thermodynamical stability of self-gravitating systems in Newtonian gravity and general relativity.

We study the statistical mechanics of classical self-gravitating systems confined within a box of radius $R$ in general relativity. It has been found that the caloric curve $T_{\infty}(E)$ has the form of a double spiral whose shape depends on the compactness parameter $\nu=GNm/Rc^2$. The double spiral shrinks as $\nu$ increases and finally disappears when $\nu_{\rm max}=0.1764$. Therefore, general relativistic effects render the system more unstable. On the other hand, the cold spiral and the hot spiral move away from each other as $\nu$ decreases. Using a normalization $\Lambda=-ER/GN^2m^2$ and $\eta=GNm^2/R k_B T_{\infty}$ appropriate to the nonrelativistic limit, and considering $\nu\rightarrow 0$, the hot spiral goes to infinity and the caloric curve tends towards a limit curve (determined by the Emden equation) exhibiting a single cold spiral, as found in former works. Using another normalization ${\cal M}=GM/Rc^2$ and ${\cal B}={Rc^4}/{GNk_B T_{\infty}}$ appropriate to the ultrarelativistic limit, and considering $\nu\rightarrow 0$, the cold spiral goes to infinity and the caloric curve tends towards a limit curve (determined by the general relativistic Emden equation) exhibiting a single hot spiral. This result is new. We discuss the analogies and the differences between this asymptotic caloric curve and the caloric curve of the self-gravitating black-body radiation. Finally, we compare box-confined isothermal models with heavily truncated isothermal distributions in Newtonian gravity and general relativity.

We determine the caloric curves of classical self-gravitating systems at statistical equilibrium in general relativity. In the classical limit, the caloric curves of a self-gravitating gas depend on a unique parameter $\nu=GNm/Rc^2$, called the compactness parameter, where $N$ is the particle number and $R$ the system's size. Typically, the caloric curves have the form of a double spiral. The "cold spiral", corresponding to weakly relativistic configurations, is a generalization of the caloric curve of nonrelativistic classical self-gravitating systems. The "hot spiral'", corresponding to strongly relativistic configurations, is similar (but not identical) to the caloric curve of the ultrarelativistic self-gravitating black-body radiation. We introduce two types of normalization of energy and temperature in order to obtain asymptotic caloric curves describing respectively the cold and the hot spirals in the limit $\nu\rightarrow 0$. As the number of particles increases, the cold and the hot spirals approach each other, merge at $\nu'_S=0.128$, form a loop above $\nu_S=0.1415$, reduce to a point at $\nu_{\rm max}=0.1764$, and finally disappear. Therefore, the double spiral shrinks when the compactness parameter $\nu$ increases, implying that general relativistic effects render the system more unstable. We discuss the nature of the gravitational collapse at low and high energies with respect to a dynamical (fast) or a thermodynamical (slow) instability.

We discuss the occurrence of gravitational phase transitions and instabilities in a gas of self-gravitating fermions within the framework of general relativity. In the classical (nondegenerate) limit, the system undergoes a gravitational collapse at low energies $EN_{\rm OV}$, there can be a subsequent gravitational collapse below a lower critical energy $E

For a useful class of functions (containing functions whose one finite component is essentially a matrix coefficient of a supercuspidal representation), we establish three results about the unipotent contribution of the Guo-Jacquet relative trace formula for the pair $(GL_n(D),GL_n(E))$. First we get a fine expansion in terms of global nilpotent integrals. Second we express these nilpotent integrals in terms of zeta integrals. Finally we prove that they satisfy certain homogeneity properties. The proof is based on a new kind of truncation introduced in a previous article.

In the last decades, large datasets of fundus photographs have been collected in diabetic retinopathy (DR) screening networks. Through deep learning, these datasets were used to train automatic detectors for DR and a few other frequent pathologies, with the goal to automate screening. One challenge limits the adoption of such systems so far: automatic detectors ignore rare conditions that ophthalmologists currently detect, such as papilledema or anterior ischemic optic neuropathy. The reason is that standard deep learning requires too many examples of these conditions. However, this limitation can be addressed with few-shot learning, a machine learning paradigm where a classifier has to generalize to a new category not seen in training, given only a few examples of this category. This paper presents a new few-shot learning framework that extends convolutional neural networks (CNNs), trained for frequent conditions, with an unsupervised probabilistic model for rare condition detection. It is based on the observation that CNNs often perceive photographs containing the same anomalies as similar, even though these CNNs were trained to detect unrelated conditions. This observation was based on the t-SNE visualization tool, which we decided to incorporate in our probabilistic model. Experiments on a dataset of 164,660 screening examinations from the OPHDIAT screening network show that 37 conditions, out of 41, can be detected with an area under the ROC curve (AUC) greater than 0.8 (average AUC: 0.938). In particular, this framework significantly outperforms other frameworks for detecting rare conditions, including multitask learning, transfer learning and Siamese networks, another few-shot learning solution. We expect these richer predictions to trigger the adoption of automated eye pathology screening, which will revolutionize clinical practice in ophthalmology.

The long-term dynamics of long-range interacting $N$-body systems can generically be described by the Balescu-Lenard kinetic equation. However, for ${1D}$ homogeneous systems, this collision operator exactly vanishes by symmetry. These systems undergo a kinetic blocking, and cannot relax as a whole under ${1/N}$ resonant effects. As a result, these systems can only relax under ${1/N^{2}}$ effects, and their relaxation is drastically slowed down. In the context of the homogeneous Hamiltonian Mean Field model, we present a new, closed and explicit kinetic equation describing self-consistently the very long-term evolution of such systems, in the limit where collective effects can be neglected, i.e. for dynamically hot initial conditions. We show in particular how that kinetic equation satisfies an $H$-Theorem that guarantees the unavoidable relaxation to the Boltzmann equilibrium distribution. Finally, we illustrate how that kinetic equation quantitatively matches with the measurements from direct $N$-body simulations., Comment: 15 pages, 4 figures, submitted to PRE

We consider the possibility that dark matter halos are made of quantum particles such as fermions or bosons in the form of Bose-Einstein condensates. In that case, they generically have a "core-halo" structure with a quantum core that depends on the type of particle considered and a halo that is relatively independent of the dark matter particle and that is similar to the NFW profile of cold dark matter. We model the halo by an isothermal gas with an effective temperature $T$. We then derive the core mass -- halo mass relation $M_c(M_v)$ of dark matter halos from an effective thermodynamical model by extremizing the free energy $F(M_c)$ with respect to the core mass $M_c$. We obtain a general relation that is equivalent to the "velocity dispersion tracing" relation according to which the velocity dispersion in the core $v_c^2\sim GM_c/R_c$ is of the same order as the velocity dispersion in the halo $v_v^2\sim GM_v/r_v$. We provide therefore a justification of this relation from thermodynamical arguments. In the case of fermions, we obtain a relation $M_c\propto M_v^{1/2}$ that agrees with the relation found numerically by Ruffini {\it et al.}. In the case of noninteracting bosons, we obtain a relation $M_c\propto M_v^{1/3}$ that agrees with the relation found numerically by Schive {\it et al.}. In the case of bosons with a repulsive self-interaction in the Thomas-Fermi limit, we predict a relation $M_c\propto M_v^{2/3}$ that still has to be confirmed numerically. We also obtain a general approximate core mass -- halo mass relation that is valid for bosons with arbitrary repulsive or attractive self-interaction. For an attractive self-interaction, we determine the maximum halo mass that can harbor a stable quantum core (dilute axion "star").