Regularity of weak minimizers of the K-energy and applications to properness and K-stability

Let $(X,\omega)$ be a compact K\"ahler manifold and $\mathcal H$ the space of K\"ahler metrics cohomologous to $\omega$. If a cscK metric exists in $\mathcal H$, we show that all finite energy minimizers of the extended K-energy are smooth cscK metrics, partially confirming a conjecture of Y.A. Rubinstein and the second author. As an immediate application, we obtain that existence of a cscK metric in $\mathcal H$ implies J-properness of the K-energy, thus confirming one direction of a conjecture of Tian. Exploiting this properness result we prove that an ample line bundle $(X,L)$ admitting a cscK metric in $c_1(L)$ is $K$-polystable.Comment: v1 Comments welcome v2 New introduction and references added v3 Final version. Preliminaries section added. Some notation changed. No other change

Protein Delivery of an Artificial Transcription Factor Restores Widespread Ube3a Expression in an Angelman Syndrome Mouse Brain.

Angelman syndrome (AS) is a neurological genetic disorder caused by loss of expression of the maternal copy of UBE3A in the brain. Due to brain-specific genetic imprinting at this locus, the paternal UBE3A is silenced by a long antisense transcript. Inhibition of the antisense transcript could lead to unsilencing of paternal UBE3A, thus providing a therapeutic approach for AS. However, widespread delivery of gene regulators to the brain remains challenging. Here, we report an engineered zinc finger-based artificial transcription factor (ATF) that, when injected i.p. or s.c., crossed the blood-brain barrier and increased Ube3a expression in the brain of an adult mouse model of AS. The factor displayed widespread distribution throughout the brain. Immunohistochemistry of both the hippocampus and cerebellum revealed an increase in Ube3a upon treatment. An ATF containing an alternative DNA-binding domain did not activate Ube3a. We believe this to be the first report of an injectable engineered zinc finger protein that can cause widespread activation of an endogenous gene in the brain. These observations have important implications for the study and treatment of AS and other neurological disorders

Renormalization and Quantum Scaling of Frenkel-Kontorova Models

We generalise the classical Transition by Breaking of Analyticity for the class of Frenkel-Kontorova models studied by Aubry and others to non-zero Planck's constant and temperature. This analysis is based on the study of a renormalization operator for the case of irrational mean spacing using Feynman's functional integral approach. We show how existing classical results extend to the quantum regime. In particular we extend MacKay's renormalization approach for the classical statistical mechanics to deduce scaling of low frequency effects and quantum effects. Our approach extends the phenomenon of hierarchical melting studied by Vallet, Schilling and Aubry to the quantum regime.Comment: 14 pages, 1 figure, submitted to J.Stat.Phy

Plasma Dynamics

Contains reports on eight research projects split into two sections.National Science Foundation (Grant ENG79-07047)U.S. Air Force - Office of Scientific Research (Grant AFOSR-77-3143D)U.S. Department of Energy (Contract DE-ACO2-78ET-51013)U.S. Department of Energy (Contract DE-ACO2-78ET-53073.AO02)U.S. Department of Energy (Contract DE-ACO2-78ET-53074)U.S. Department of Energy (Contract DE-ACO2-78ET-53076)U.S. Department of Energy (Contract DE-ACO2-78ET-51002

Studying complex interventions : reflections from the FEMHealth project on evaluating fee exemption policies in West Africa and Morocco

Peer reviewedPublisher PD

Atom Interferometers

Interference with atomic and molecular matter waves is a rich branch of atomic physics and quantum optics. It started with atom diffraction from crystal surfaces and the separated oscillatory fields technique used in atomic clocks. Atom interferometry is now reaching maturity as a powerful art with many applications in modern science. In this review we first describe the basic tools for coherent atom optics including diffraction by nanostructures and laser light, three-grating interferometers, and double wells on AtomChips. Then we review scientific advances in a broad range of fields that have resulted from the application of atom interferometers. These are grouped in three categories: (1) fundamental quantum science, (2) precision metrology and (3) atomic and molecular physics. Although some experiments with Bose Einstein condensates are included, the focus of the review is on linear matter wave optics, i.e. phenomena where each single atom interferes with itself.Comment: submitted to Reviews of Modern Physic