The Infinity Laplacian eigenvalue problem: reformulation and a numerical scheme

In this work we present an alternative formulation of the higher eigenvalue problem associated to the infinity Laplacian, which opens the door for numerical approximation of eigenfunctions. A rigorous analysis is performed to show the equivalence of the new formulation to the traditional one. We define consistent numerical schemes for approximating infinity ground states and higher eigenfunctions and perform numerical experiments which also shed light on some open conjectures in the field.Comment: 20 pages, 8 figure

Induced congenital diaphragmatic hernia: a model in rats

The objectives of this thesis are to: 1. Compare the induced CDH in rats with the human situation and other available animal models. 2. Describe the morphological characteristics of the developing rat lung and diaphragm in congenital diaphragmatic hernia compared with controls. 3. Evaluate the suitability of this model in testing different ventilatory modes and the subsequent reaction of the CDH lung from a biochemical and histological point of view

CLIP: Cheap Lipschitz Training of Neural Networks

Despite the large success of deep neural networks (DNN) in recent years, most neural networks still lack mathematical guarantees in terms of stability. For instance, DNNs are vulnerable to small or even imperceptible input perturbations, so called adversarial examples, that can cause false predictions. This instability can have severe consequences in applications which influence the health and safety of humans, e.g., biomedical imaging or autonomous driving. While bounding the Lipschitz constant of a neural network improves stability, most methods rely on restricting the Lipschitz constants of each layer which gives a poor bound for the actual Lipschitz constant. In this paper we investigate a variational regularization method named CLIP for controlling the Lipschitz constant of a neural network, which can easily be integrated into the training procedure. We mathematically analyze the proposed model, in particular discussing the impact of the chosen regularization parameter on the output of the network. Finally, we numerically evaluate our method on both a nonlinear regression problem and the MNIST and Fashion-MNIST classification databases, and compare our results with a weight regularization approach.Comment: 12 pages, 2 figures, accepted at SSVM 202

播磨・西摂の計画古道と条里

markdownabstractAbstract 16 patients underwent acute hypervolaemic haemodilution with dextran 40 and Ringers lactate, to see whether this procedure could avoid preoperative blood transfusion. Packed cell volume (PCV) and oxygen extraction decreased, and cardiac index and pulmonary wedge pressure increased, although end-systolic area was unchanged. PCV was not significantly different between patients who lost less than or greater than 20% of their initial blood volume. This preoperative manoeuvre, which reduces loss of red blood cells, allowed major surgery to be completed safely without blood transfusion

Evaluation of lung function changes before and after surfactant application during artificial ventilation in newborn rats with congenital diaphragmatic hernia

Patients with congenital diaphragmatic hernia (CDH) have unilateral or bilateral hypoplasia of the lungs including delayed maturation of the terminal air sacs. Because these lungs are highly susceptible to barotrauma and oxygen toxicity, even in full-term newborns, continued research into optimal ventilatory regimen is essential to improve survival rate and to prevent ongoing lung damage. Against this background, the effect of exogenous surfactant application is evaluated. In newborn rats, CDH was induced after a single dose of 2,4 dichloro-4'-nitrophenyl (Nitrofen) (400 mg/kg) on day 10 of gestation. The newborn rats were intubated immediately after hysterotomy, transferred to a heated multichambered body plethysmograph, and artificially ventilated. Inspiratory peak pressures were initially set at 17 cm H2O, with positive end-expiratory pressure at 0 cm H2O and FIO2at 1.0. The pressure was raised in steps of 5 cm H2O, from 5 to 30 cm H2O, to obtain pressure- volume diagrams at 0, 1, and 6 hours of artificial ventilation. These measurements were obtained in controls and in CDH rats with and without endotracheal installation of bovine surfactant (n = 4 to 10 in each group). Significant differences in lung volume between CDH and control rats were observed at all time-points. Surfactant application had a positive effect on lung volume, especially in control rats at t = 1 hour. No significant differences were observed between the CDH groups at t = 1 or t = 6 hours. In this animal model, the effect of artificial ventilation as well as the beneficial short-term effect of exogenous surfactant application have been evaluated. A continued positive effect on lung volume in CDH lungs could not be determined. Routine administration of exogenous surfactant in human CDH patients is not supported by these experimental results