A nonabelian trace formula

Let $E/F$ be an extension of number fields with $\mathrm{Gal}(E/F)$ simple and nonabelian. In [G] the first named author suggested an approach to nonsolvable base change and descent of automorphic representations of $\mathrm{GL}_2$ along such an extension. Motivated by this we prove a trace formula whose spectral side is a weighted sum over cuspidal automorphic representations of $\mathrm{GL}_2(\mathbb{A}_E)$ that are isomorphic to their $\mathrm{Gal}(E/F)$-conjugates.Comment: Comments are welcom

Evidence from the wider use of the BSL Receptive Skills Test

Following the development and standardization of the British Sign Language (BSL) Receptive Skills Test (Herman et al., 1999), the test was made widely available to professionals working with deaf children. Test users were asked to return completed score-sheets on individual children they had tested in order to compare a selection of children from the wider population of deaf children with those from the sample upon whom the test was standardized. The analysis of almost 200 score sheets is presented. Overall, children from the wider population achieved lower standard scores than those from the standardization sample, with the exception of native signers, whose scores were equivalent to the native signers' scores in the original sample. The findings raise important questions about the adequacy of BSL provision for deaf children in hearing families. Data on tester ratings and children's reading scores provide an opportunity for a preliminary investigation of the psychometric properties of the test. Finally, tester feedback on the test itself, the training offered and the overall contribution of the test to assessing deaf children's BSL development are reviewed

Forebrain Origins of Glutamatergic Innervation to the Rat Paraventricular Nucleus of the Hypothalamus: Differential Inputs to the Anterior Versus Posterior Subregions

The hypothalamic paraventricular nucleus (PVN) regulates numerous homeostatic systems and functions largely under the influence of forebrain inputs. Glutamate is a major neurotransmitter in forebrain, and glutamate neurosignaling in the PVN is known to mediate many of its functions. Previous work showed that vesicular glutamate transporters (VGluTs; specific markers for glutamatergic neurons) are expressed in forebrain sites that project to the PVN; however, the extent of this presumed glutamatergic innervation to the PVN is not clear. In the present study retrograde FluoroGold (FG) labeling of PVN-projecting neurons was combined with in situ hybridization for VGluT1 and VGluT2 mRNAs to identify forebrain regions that provide glutamatergic innervation to the PVN and its immediate surround in rats, with special consideration for the sources to the anterior versus posterior PVN. VGluT1 mRNA colocalization with retrogradely labeled FG neurons was sparse. VGluT2 mRNA colocalization with FG neurons was most abundant in the ventromedial hypothalamus after anterior PVN FG injections, and in the lateral, posterior, dorsomedial, and ventromedial hypothalamic nuclei after posterior PVN injections. Anterograde tract tracing combined with VGluT2 immunolabeling showed that 1) ventromedial nucleus-derived glutamatergic inputs occur in both the anterior and posterior PVN; 2) posterior nucleus-derived glutamatergic inputs occur predominantly in the posterior PVN; and 3) medial preoptic nucleus-derived inputs to the PVN are not glutamatergic, thereby corroborating the innervation pattern seen with retrograde tracing. The results suggest that PVN subregions are influenced by varying amounts and sources of forebrain glutamatergic regulation, consistent with functional differentiation of glutamate projections. J. Comp. Neurol. 519:1301–1319, 2011. © 2010 Wiley-Liss, Inc