On the approximation of extreme quantiles with neural networks

National audienceIn this study, we propose a new parametrization for the generator of a Generative adversarial network (GAN) adapted to data from heavy-tailed distributions. We provide an analysis of the uniform error between an extreme quantile and its GAN approximation. Numerical experiments are conducted both on real and simulated data.Dans cette étude nous proposons une nouvelle paramétrisation du générateur d'un réseau antagoniste génératif (GAN) adaptée aux données issues d'une distribution a queue lourde. Nous apportons une analyse de l'erreur d'approximation en norme uniforme d'un quantile extrême par le GAN ainsi construit. Des simulations numériques sont réalisées sur des données réelles et simulées. Mots-clés. Théorie des valeurs extrêmes, réseau de neurones, modèle génératif

A refined Weissman estimator for extreme quantiles

International audienceWeissman extrapolation methodology for estimating extreme quantiles from heavy-tailed distributions is based on two estimators: an order statistic to estimate an intermediate quantile and an estimator of the tail-index. The common practice is to select the same intermediate sequence for both estimators. In this work, we show how an adapted choice of two different intermediate sequences leads to a reduction of the asymptotic bias associated with the resulting refined Weissman estimator. The asymptotic normality of the latter estimator is established and a data-driven method is introduced for the practical selection of the intermediate sequences. Our approach is compared to Weissman estimator and to six bias reduced estimators of extreme quantiles on a large scale simulation study. It appears that the refined Weissman estimator outperforms its competitors in a wide variety of situations, especially in the challenging high bias cases. Finally, an illustration on an actuarial real data set is provided

Morphometric, hemodynamic, and biomechanical factors influencing blood flow and oxygen concentration in the human lamina cribrosa

Purpose: We developed a combined biomechanical and hemodynamic model of the human eye to estimate blood flow and oxygen concentration within the lamina cribrosa (LC) and rank the factors that influence LC oxygen concentration. Methods: We generated 5000 finite-element eye models with detailed microcapillary networks of the LC and computed the oxygen concentration of the lamina retinal ganglion cell axons. For each model, we varied the intraocular pressure (IOP) from 10 mm Hg to 55 mm Hg in 5-mm Hg increments, the cerebrospinal fluid pressure (13 ± 2 mm Hg), cup depth (0.2 ± 0.1 mm), scleral stiffness (±20% of the mean values), LC stiffness (0.41 ± 0.2 MPa), LC radius (1.2 ± 0.12 mm), average LC pore size (5400 ± 2400 µm2), the microcapillary arrangement (radial, isotropic, or circumferential), and perfusion pressure (50 ± 9 mm Hg). Blood flow was assumed to originate from the LC periphery and drain via the central retinal vein. Finally, we performed linear regressions to rank the influence of each factor on the LC tissue oxygen concentration. Results: LC radius and perfusion pressure were the most important factors in influencing the oxygen concentration of the LC. IOP was another important parameter, and eyes with higher IOP had higher compressive strain and slightly lower oxygen concentration. In general, superior–inferior regions of the LC had significantly lower oxygen concentration than the nasal–temporal regions, resulting in an hourglass pattern of oxygen deficiency. Conclusions: To the best of our knowledge, this study is the first to implement a comprehensive hemodynamical model of the eye that accounts for the biomechanical forces and morphological parameters of the LC. The results provide further insight into the possible relationship of biomechanical and vascular pathways leading to ischemia-induced optic neuropathy

Comparisons of day-time and night-time hydroacoustic surveys in temperate lakes

In recent years, due to an increased need for non-intrusive sampling techniques, hydroacoustics has attracted attention in fishery science and management. Efforts to promote standardisation are increasing the accuracy, efficiency, and comparability of this method. The European Water Framework Directive and the Standard Operating Procedures for Fisheries Hydroacoustic Surveys in North American Great Lakes has recommended that surveys be conducted at night. At night, fish usually disperse in the water column, thus allowing for single echo detection and subsequent accurate fish size estimation, while day-time schooling behaviour hampers the estimation of fish size. However, sampling during the day would often be safer and cheaper. This study analyses how fisheries hydroacoustic results differ between day-time and night-time surveys, using data from 14 natural temperate lakes of various size. Data collected during the day and night at two depth layers linked to thermal stratification were compared in terms of acoustic scattering strength, target strength, and biomass estimates. The results showed a significant correlation between day-time and night-time estimates, though biomass in the upper layer was biased for day-time surveys, mainly due to incorrect fish size estimates resulting from rare single echo detections and schooling behaviour. Biomass estimates for the lower depth layer did not significantly differ between the two diel periods. Thus, this study confirms that hydroacoustic sampling in temperate lakes should be performed at night for accurate fish stock biomass estimates

Effect of changing heart rate on the ocular pulse and dynamic biomechanical behavior of the optic nerve head

Purpose: To study the effect of changing heart rate on the ocular pulse and the dynamic biomechanical behavior of the optic nerve head (ONH) using a comprehensive mathematical model. Methods: In a finite element model of a healthy eye, a biphasic choroid consisted of a solid phase with connective tissues and a fluid phase with blood, and the lamina cribrosa (LC) was viscoelastic as characterized by a stress-relaxation test. We applied arterial pressures at 18 ocular entry sites (posterior ciliary arteries), and venous pressures at four exit sites (vortex veins). In the model, the heart rate was varied from 60 to 120 bpm (increment: 20 bpm). We assessed the ocular pulse amplitude (OPA), pulse volume, ONH deformations, and the dynamic modulus of the LC at different heart rates. Results: With an increasing heart rate, the OPA decreased by 0.04 mm Hg for every 10 bpm increase in heart rate. The ocular pulse volume decreased linearly by 0.13 µL for every 10 bpm increase in heart rate. The storage modulus and the loss modulus of the LC increased by 0.014 and 0.04 MPa, respectively, for every 10 bpm increase in heart rate. Conclusions: In our model, the OPA, pulse volume, and ONH deformations decreased with an increasing heart rate, whereas the LC became stiffer. The effects of blood pressure/heart rate changes on ONH stiffening may be of interest for glaucoma pathology

DeshadowGAN: a deep learning approach to remove shadows from optical coherence tomography images

Purpose: To remove blood vessel shadows from optical coherence tomography (OCT) images of the optic nerve head (ONH). Methods: Volume scans consisting of 97 horizontal B-scans were acquired through the center of the ONH using a commercial OCT device for both eyes of 13 subjects. A custom generative adversarial network (named DeshadowGAN) was designed and trained with 2328 B-scans in order to remove blood vessel shadows in unseen B-scans. Image quality was assessed qualitatively (for artifacts) and quantitatively using the intralayer contrast—a measure of shadow visibility ranging from 0 (shadow-free) to 1 (strong shadow). This was computed in the retinal nerve fiber layer (RNFL), the inner plexiform layer (IPL), the photoreceptor (PR) layer, and the retinal pigment epithelium (RPE) layer. The performance of DeshadowGAN was also compared with that of compensation, the standard for shadow removal. Results: DeshadowGAN decreased the intralayer contrast in all tissue layers. On average, the intralayer contrast decreased by 33.7 ± 6.81%, 28.8 ± 10.4%, 35.9 ± 13.0%, and 43.0 ± 19.5% for the RNFL, IPL, PR layer, and RPE layer, respectively, indicating successful shadow removal across all depths. Output images were also free from artifacts commonly observed with compensation. Conclusions: DeshadowGAN significantly corrected blood vessel shadows in OCT images of the ONH. Our algorithm may be considered as a preprocessing step to improve the performance of a wide range of algorithms including those currently being used for OCT segmentation, denoising, and classification. Translational Relevance: DeshadowGAN could be integrated to existing OCT devices to improve the diagnosis and prognosis of ocular pathologies

Reduction of the Lamina Cribrosa Curvature After Trabeculectomy in Glaucoma

PURPOSE. To investigate whether the lamina cribrosa (LC) curvature is decreased after trabeculectomy. METHODS. Thirty-nine eyes of 39 patients with primary open-angle glaucoma who underwent trabeculectomy were included. Optic nerves were scanned by using enhanced-depth-imaging spectral-domain optical coherence tomography before and after trabeculectomy. The LC curvature was assessed by measuring the LC curvature index (LCCI) in seven horizontal Bscan images in each eye. RESULTS. The LCCI was significantly smaller at postoperative 6 months than at the preoperative level in all seven planes (all P < 0.001). Preoperative LCCI was associated with younger age at superior midperiphery, midhorizontal plane, inferior midperiphery (all P 0.005) and higher preoperative intraocular pressure (IOP) at superior and inferior midperiphery (both P ¼ 0.039). Younger age and larger preoperative LCCI were associated with a larger reduction of the LCCI at all three locations (P ¼ 0.003 and 0.031 at superior midperiphery, P ¼ 0.011 and 0.001 at midhorizontal plane, and P ¼ 0.014 and 0.005 at inferior midperiphery, respectively), whereas the percentage IOP lowering was associated at superior and inferior midperiphery (P ¼ 0.017 and 0.047, respectively). CONCLUSIONS. Lamina cribrosa curvature was reduced after trabeculectomy. This finding suggests that LC curvature may have value as a parameter relevant to optic nerve head biomechanics

A multi-site campaign to measure solar-like oscillations in Procyon. II. Mode frequencies

We have analyzed data from a multi-site campaign to observe oscillations in the F5 star Procyon. The data consist of high-precision velocities that we obtained over more than three weeks with eleven telescopes. A new method for adjusting the data weights allows us to suppress the sidelobes in the power spectrum. Stacking the power spectrum in a so-called echelle diagram reveals two clear ridges that we identify with even and odd values of the angular degree (l=0 and 2, and l=1 and 3, respectively). We interpret a strong, narrow peak at 446 muHz that lies close to the l=1 ridge as a mode with mixed character. We show that the frequencies of the ridge centroids and their separations are useful diagnostics for asteroseismology. In particular, variations in the large separation appear to indicate a glitch in the sound-speed profile at an acoustic depth of about 1000 s. We list frequencies for 55 modes extracted from the data spanning 20 radial orders, a range comparable to the best solar data, which will provide valuable constraints for theoretical models. A preliminary comparison with published models shows that the offset between observed and calculated frequencies for the radial modes is very different for Procyon than for the Sun and other cool stars. We find the mean lifetime of the modes in Procyon to be 1.29 +0.55/-0.49 days, which is significantly shorter than the 2-4 days seen in the Sun.Comment: accepted for publication in Ap