Area spectrum of the Schwarzschild black hole

We consider a Hamiltonian theory of spherically symmetric vacuum Einstein gravity under Kruskal-like boundary conditions in variables associated with the Einstein-Rosen wormhole throat. The configuration variable in the reduced classical theory is the radius of the throat, in a foliation that is frozen at the left hand side infinity but asymptotically Minkowski at the right hand side infinity, and such that the proper time at the throat agrees with the right hand side Minkowski time. The classical Hamiltonian is numerically equal to the Schwarzschild mass. Within a class of Hamiltonian quantizations, we show that the spectrum of the Hamiltonian operator is discrete and bounded below, and can be made positive definite. The large eigenvalues behave asymptotically as~$\sqrt{2k}$, where $k$ is an integer. The resulting area spectrum agrees with that proposed by Bekenstein and others. Analogous results hold in the presence of a negative cosmological constant and electric charge. The classical input that led to the quantum results is discussed.Comment: 30 pages, REVTeX v3.0. (Minor additions, several added references.

Genomic sequencing of meningiomas identifies oncogenic SMO and AKT1 mutations

Meningiomas are the most common primary nervous system tumor. The tumor suppressor NF2 is disrupted in approximately half of meningiomas1 but the complete spectrum of genetic changes remains undefined. We performed whole-genome or whole-exome sequencing on 17 meningiomas and focused sequencing on an additional 48 tumors to identify and validate somatic genetic alterations. Most meningiomas exhibited simple genomes, with fewer mutations, rearrangements, and copy-number alterations than reported in other adult tumors. However, several meningiomas harbored more complex patterns of copy-number changes and rearrangements including one tumor with chromothripsis. We confirmed focal NF2 inactivation in 43% of tumors and found alterations in epigenetic modifiers among an additional 8% of tumors. A subset of meningiomas lacking NF2 alterations harbored recurrent oncogenic mutations in AKT1 (E17K) and SMO (W535L) and exhibited immunohistochemical evidence of activation of their pathways. These mutations were present in therapeutically challenging tumors of the skull base and higher grade. These results begin to define the spectrum of genetic alterations in meningiomas and identify potential therapeutic targets

Tau 6D and 6P isoforms inhibit polymerization of full-length tau in vitro

Alzheimer\u27s disease and other tauopathies are characterized by the intracellular accumulation of insoluble filaments of the microtubule-associated protein tau. The six canonical tau isoforms in the adult brain consist of an N-terminal projection domain followed by a proline-rich region, a microtubule-binding repeat region, and a C-terminal tail. However, alternative splicing in exon 6 produces an additional set of tau isoforms, termed 6D and 6P, which contain only the N-terminus and part of the proline-rich region. We have previously shown that constructs representing N-terminal fragments of tau, which resemble the naturally occurring 6P and 6D isoforms, inhibit polymerization of the full-length protein in an in vitro filament formation assay and traced the inhibitory activity to amino acids 18-42. Here we report that 6P and 6D tau isoforms inhibit polymerization of full-length tau (hTau40) in a similar manner, likely by stabilizing full-length tau in a soluble conformation. The absence of exons 2 and 3 decreased the effectiveness of the 6D isoforms but not the 6P variants or the N-terminal tau fragments from our previous study, indicating that the 18-42 region is not the sole determinant of inhibitory ability. Finally, this paper demonstrates that inhibition is blocked by pseudophosphorylation of tyrosines 18 and 29, providing a potential link between tyrosine phosphorylation and disease progression. Taken together, these results indicate that the 6P/6D isoforms are potential endogenous inhibitors of tau filament formation and suggest a mechanism by which this ability may be disrupted in disease