Random walk on the Poincaré disk induced by a group of Möbius transformations.

We consider a discrete-time random motion, Markov chain on the Poincaré disk. In the basic variant of the model a particle moves along certain circular arcs within the disk, its location is determined by a composition of random Möbius transformations. We exploit an isomorphism between the underlying group of Möbius transformations and to study the random motion through its relation to a one-dimensional random walk.

The relationship between Gulf War illness, brain N-acetylaspartate, and post-traumatic stress disorder.

A previous study (Haley RW, Marshall WW, McDonald GG, Daugherty MA, Petty F, Fleckenstein JL: Brain abnormalities in Gulf War syndrome: evaluation with 1H MR spectroscopy. Radiology 2000; 215: 807-817) suggested that individuals with Gulf War Illness (GWI) had reduced quantities of the neuronal marker N-acetylaspartate (NAA) in the basal ganglia and pons. This study aimed to determine whether NAA is reduced in these regions and to investigate correlations with other possible causes of GWI, such as psychological response to stress in a large cohort of Gulf War veterans.

Improved standards for laboratory animals?

In February 1993, Judge Charles R. Richey of the United States District Court issued a summary judgment in the case of Animal Legal Defense Fund, et al. v.