Quantum Dilaton Gravity in the Light-cone Gauge

Recently, models of two-dimensional dilaton gravity have been shown to admit classical black-hole solutions that exhibit Hawking radiation at the semi-classical level. These classical and semi-classical analyses have been performed in conformal gauge. We show in this paper that a similar analysis in the light--cone gauge leads to the same results. Moreover, quantization of matter fields in light--cone gauge can be naturally extended to include quantizing the metric field {\it \`a la} KPZ. We argue that this may provide a new framework to address many issues associated to black-hole physics.Comment: 16 pages, Use phyzzx, CERN-TH.6633/9

Evans v. Michigan: The Impact of Judicial Error on Double Jeopardy Protection

This commentary previews an upcoming Supreme Court case, Evans v. Michigan, in which the Court has an opportunity to clarify the bounds of the prohibition on double jeopardy. More specifically, the Court will determine what, if any, impact judicial error has on double jeopardy protection under the Fifth Amendment

Singularities and the Finale of Black Hole Evaporation

In this essay we argue that once quantum gravitational effects change the classical geometry of a black hole and remove the curvature singularity, the black hole would not evaporate entirely but approach a remnant. In a modified Schwarzschild spacetime characterized by a finite Kretschmann scalar, a minimal mass of the black hole is naturally bounded by the existence of the horizon rather than introduced by hand. A thermodynamical analysis discloses that the temperature, heat capacity and the luminosity are vanishing naturally when the black hole mass approaches the minimal value. This phenomenon may be attributed to the existence of the minimal length in quantum gravity. It can also be understood heuristically by connecting the generalized uncertainty principle with the running of Newton's gravitational constant.Comment: 10 page

Chiral Iron-N4-Complexes for Asymmetric C-H Aminations

Due to iron's low toxicity and abundance on Earth, chiral inexpensive metallic iron catalysts have gained great attention. There are still no examples of the direct use of simple and readily available chiral iron catalysts to catalyse the activation of C-H bonds to enantioselectively form C-N bonds. This thesis is based on the enantioselective catalytic amination of challenging secondary and tertiary C-H bonds via chiral N4 iron catalysts. At the same time, the enantioselective amination produces a series of unnatural α-amino acids. A novel approach for synthesizing α-amino acids is disclosed. In the first two sections, a series of chiral N4 iron catalysts were synthesized and successfully applied to asymmetric secondary C-H bonds amination reactions. Our method employs abundant and easily accessible carboxylic acids as starting materials, which are connected to a nitrogenation reagent, followed by a highly regio- and enantioselective iron-catalyzed C(sp3)-H amination. This straightforward method displays a broad scope, providing rapid access to optically active α-amino acids with aryl, allyl, and alkyl side chains, and also permits stereocontrolled late-stage amination of carboxylic acid-containing drugs and natural products. In the third section, A straightforward two-step synthesis of non-racemic α,α-disubstituted α-amino acids by an enantioconvergent 1,3-migratory nitrene C(sp3)-H insertion is reported. Readily available racemic α-branched carboxylic acids are DCC/EDCI-coupled to provide racemic azanyl esters which undergo a rearrangement into non-racemic N-Troc-protected α,α-disubstituted α-amino acids catalyzed by an easy to store and robust chiral iron catalyst. α,α-Disubstituted α-amino acids with one aryl group in α-position are provided in yields of up to 99% and with up to 88% ee. Selected examples demonstrate that recrystallization can improve the enantiomeric excess to 99% ee

A multi-protein receptor-ligand complex underlies combinatorial dendrite guidance choices in C. elegans.

Ligand receptor interactions instruct axon guidance during development. How dendrites are guided to specific targets is less understood. The C. elegans PVD sensory neuron innervates muscle-skin interface with its elaborate dendritic branches. Here, we found that LECT-2, the ortholog of leukocyte cell-derived chemotaxin-2 (LECT2), is secreted from the muscles and required for muscle innervation by PVD. Mosaic analyses showed that LECT-2 acted locally to guide the growth of terminal branches. Ectopic expression of LECT-2 from seam cells is sufficient to redirect the PVD dendrites onto seam cells. LECT-2 functions in a multi-protein receptor-ligand complex that also contains two transmembrane ligands on the skin, SAX-7/L1CAM and MNR-1, and the neuronal transmembrane receptor DMA-1. LECT-2 greatly enhances the binding between SAX-7, MNR-1 and DMA-1. The activation of DMA-1 strictly requires all three ligands, which establishes a combinatorial code to precisely target and pattern dendritic arbors