Anti-eikonal equation of an eigenmirror.

We call a surface that appears undistorted when viewed in a curved mirror an eigensurface and the mirror an eigenmirror. Such pairs are described by a first-order nonlinear partial differential equation of the form ++++2+2=0, where =(,,), which we call the anti-eikonal equation. We give examples of symbolic and numerical solutions, including pairs that are geometrically congruent.

Eigensurfaces of eigenmirrors.

Typically, if an observer gazes at a curved reflector, the objects in it will appear to be distorted. We show here that for some mirrors there exist surfaces that do not appear distorted when viewed from a prescribed location. We call such mirrors eigenmirrors and the surfaces eigensurfaces.

Solitary waves in diatomic chains.

We consider the mechanism of formation of isolated localized wave structures in the diatomic Fermi-Pasta-Ulam (FPU) model. Using a singular multiscale asymptotic analysis in the limit of high mass mismatch between the alternating elements, we obtain the typical slow-fast time scale separation and formulate the Fredholm orthogonality condition approximating a sequence of mass ratios supporting the formation of solitary waves in the general type of diatomic FPU models. This condition is made explicit in the case of a diatomic Toda lattice.

Neural Network Prediction of ICU Length of Stay Following Cardiac Surgery Based on Pre-Incision Variables.

Background: Advanced predictive analytical techniques are being increasingly applied to clinical risk assessment. This study compared a neural network model to several other models in predicting the length of stay (LOS) in the cardiac surgical intensive care unit (ICU) based on pre-incision patient characteristics.

Methods: Thirty six variables collected from 185 cardiac surgical patients were analyzed for contribution to ICU LOS.

Double-mirror catadioptric sensors with ultrawide field of view and no distortion.

We compute a family of double-mirror catadioptric sensors with ultrawide field of view and no distortion. The two concentric mirrors are rotationally symmetric, and the inside mirror is a revolved conic section. The mapping between the object and the image planes was linear, hence the lack of distortion.