Long and short paths in uniform random recursive dags

In a uniform random recursive k-dag, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S_n is the shortest path distance from node n to the root, then we determine the constant \sigma such that S_n/log(n) tends to \sigma in probability as n tends to infinity. We also show that max_{1 \le i \le n} S_i/log(n) tends to \sigma in probability.Comment: 16 page

Coexistence of Chiari 2 malformation and moyamoya syndrome in a 17-year-old girl.

A 17-year-old female with Chiari 2 malformation developed cerebral infarction with angiographically typical bilateral moyamoya vessels manifesting as sudden onset of moderate left hemiparesis. Magnetic resonance imaging revealed multiple infarcts in the right frontal lobe, agenesis of the corpus callosum, upward herniation of the dorsal cerebellum, tectal beak of the midbrain, and downward herniation of the cerebellar vermis. Cerebral angiography demonstrated occlusion of the bilateral internal carotid arteries and basal moyamoya vessels. Single photon emission computed tomography showed significantly reduced regional cerebral blood flow in the right frontoparietal cortex. The cerebral vascular reactivity to acetazolamide was diminished in both cerebral hemispheres. She underwent superficial temporal artery-middle cerebral artery anastomosis combined with encephalo-myo-synangiosis on the right, and on the left 6 months later. Cerebral angiography performed 4 months after the second operation showed good patency of the bypasses and substantial collateral vessels in both cerebral hemispheres. This association may have happened by chance, and a common etiology is uncertain, but a currently undetermined genomic component might have contributed to the disease progression

Development of Plasma Vitellogenin Assay for Estrogenic Effects of Endocrine-Disrupting Chemicals Using Ovariectomized Goldfish (Carassius auratus)

Plasma vitellogenin (VTG) assay was developed using ovariectomized goldfish (Carassius auratus) for determining the estrogenic effects of endocrine-disrupting chemicals. In a laboratory study, we assessed the estrogenic activity of commercial fish diets by using a diet for ornamental carp (CD) and a casein-based formulated fish diet (FD), which was shown to not contain soybean or fish meal in a previous study. In ovariectomized fish, plasma VTG concentrations were significantly higher in the CD-fed group than in the FD-fed group. These results indicate that the estrogen activity of CD may be high enough to cause induction of plasma VTG in ovariectomized goldfish as previously observed in male goldfish. Moreover, the effect of estrogen on plasma VTG induction was confirmed by significant plasma VTG production following the exposure of FD-fed ovariectomized goldfish to a nominal estradiol-17β concentration of 100 μg/l for 31 days. Our data suggest that induction of plasma VTG using ovariectomized goldfish is a good tool for evaluating the estrogenic effects of endocrine-disrupting chemicals