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 ℝ to study the random motion through its relation to a one-dimensional random walk. More specifically, we show that key geometric characteristics of the random motion, such as Busemann functions and bipolar coordinates evaluated at its location, and hyperbolic distance from the origin, can be either explicitly computed or approximated in terms of the random walk. We also consider a variant of the model where the motion is not confined to a single arc, but rather the particle switches between arcs of a parabolic pencil of circles at random times.

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. Individuals underwent tests to determine their physical and psychological health and to identify veterans with (n=81) and without (n=97) GWI. When concentrations of NAA and ratios of NAA to creatine- and choline-containing metabolites were measured in the basal ganglia and pons, no significant differences were found between veterans with or without GWI, suggesting that GWI is not associated with reduced NAA in these regions. Veterans with GWI had significantly higher rates of post-traumatic stress disorder, supporting the idea that GWI symptoms are stress related.

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. The Secretary of Agriculture, et al. The decision, which was in favor of the Animal Legal Defense Fund, requires the U.S. Department of Agriculture to withdraw its current regulations governing exercise for dogs and the psychological well-being of nonhuman primates used for biomedical research and to issue new regulations containing only minimum, measurable standards. Both plaintiffs and defendants contended that they were seeking the best interests of the laboratory animals. The issue at stake is whether animals are better protected if the government establishes limited minimal standards or is allowed to require institutions to provide additional standards, which will be judged on the basis of their effectiveness in maintaining healthy animals. The Court avoided this dispute, however, by placing primary emphasis on applying the Administrative Procedures Act and stating that it was merely interpreting the "plain meaning" of the Animal Welfare Act, as amended. In this article, arguments are presented for interpreting the law in a far more flexible way than Judge Richey did. The conclusion is also reached that there were no winners in the Animal Legal Defense Fund case and that the real losers are the laboratory animals.