Exit Times, Moment Problems and Comparison Theorems

We establish comparison theorems involving exit time moments for Brownian motion and eigenvalues for the Dirichlet problem for domains in a complete Riemannian manifold. These theorems are closely related to isoperimetric properties of the ambient manifold.     

Perspective Functions: Properties,Constructions, and Examples

Many functions encountered in applied mathematics and in statistical data analysis can be expressed in terms of perspective functions. One of the earliest examples is the Fisher information, which appeared in statistics in the 1920s. We analyze various algebraic and convex-analytical properties of perspective functions and provide general schemes to construct lower semicontinuous convex functions from them. Several new examples are presented and existing instances are featured as special cases.     

A computational model for human eye-movements in military simulations

Models of eye movements of an observer searching for human targets are helpful in developing accurate models of target acquisition times and false positive detections. We develop a new model describing the distribution of gaze positions for an observer which includes both bottom-up (salience) and top-down (task dependent) factors. We validate the combined model against a bottom-up model from the literature and against the bottom up and top down parts alone using human performance data on stationary targets. The new model is shown to be significantly better. The new model requires a large amount of data about the terrain and the target that is obtained directly from the 3D simulation through an automated process.     

Does ignorance promote norm compliance?

A large extent of undetected norm violations may have positive effects for society. If many norm violations are hidden, society seems to be in good order so that actors are more willing to comply with the norms themselves. In this sense, ignorance promotes norm compliance. We challenge this view by arguing that in scenarios, in which norms are controlled and enforced by third parties who receive rewards for their success, the opposite is true: Ignorance promotes norm violations. The reason is that unsuspicious inspectors who believe that little hidden norm violations are committed will spend less effort for detection, some formerly detected norm violations will go undetected, norm targets will be less deterred from the lower detection probability and will commit more norm violations over time. This article develops a respective mathematical model and confirms the above described intuition.