Topologically non-trivial quantum layers

Given a complete non-compact surface embedded in R^3, we consider the Dirichlet Laplacian in a layer of constant width about the surface. Using an intrinsic approach to the layer geometry, we generalise the spectral results of an original paper by Duclos et al. to the situation when the surface does not possess poles. This enables us to consider topologically more complicated layers and state new spectral results. In particular, we are interested in layers built over surfaces with handles or several cylindrically symmetric ends. We also discuss more general regions obtained by compact deformations of certain layers.Comment: 15 pages, 6 figure

Pairing Neutral Cues with Alcohol Intoxication: New Findings in Executive and Attention Networks

Rationale: Alcohol-associated stimuli capture attention, yet drinkers differ in the precise stimuli that become paired with intoxication. Objectives: Extending our prior work to examine the influence of alcoholism risk factors, we paired abstract visual stimuli with intravenous alcohol delivered covertly and examined brain responses to these Pavlovian conditioned stimuli in fMRI when subjects were not intoxicated. Methods: Sixty healthy drinkers performed task-irrelevant alcohol conditioning that presented geometric shapes as conditioned stimuli. Shapes were paired with a rapidly rising alcohol limb (CS+) using intravenous alcohol infusion targeting a final peak breath alcohol concentration of 0.045 g/dL or saline (CS−) infusion at matched rates. On day two, subjects performed monetary delay discounting outside the scanner to assess delay tolerance and then underwent event-related fMRI while performing the same task with CS+, CS−, and an irrelevant symbol. Results: CS+ elicited stronger activation than CS− in frontoparietal executive/attention and orbitofrontal reward-associated networks. Risk factors including family history, recent drinking, sex, and age of drinking onset did not relate to the [CS+ > CS−] activation. Delay-tolerant choice and [CS+ > CS−] activation in right inferior parietal cortex were positively related. Conclusions: Networks governing executive attention and reward showed enhanced responses to stimuli experimentally paired with intoxication, with the right parietal cortex implicated in both alcohol cue pairing and intertemporal choice. While different from our previous study results in 14 men, we believe this paradigm in a large sample of male and female drinkers offers novel insights into Pavlovian processes less affected by idiosyncratic drug associations

A Spectral Bernstein Theorem

We study the spectrum of the Laplace operator of a complete minimal properly immersed hypersurface $M$ in $\R^{n+1}$. (1) Under a volume growth condition on extrinsic balls and a condition on the unit normal at infinity, we prove that $M$ has only essential spectrum consisting of the half line $[0, +\infty)$. This is the case when $\lim_{\tilde{r}\to +\infty}\tilde{r}\kappa_i=0$, where $\tilde{r}$ is the extrinsic distance to a point of $M$ and $\kappa_i$ are the principal curvatures. (2) If the $\kappa_i$ satisfy the decay conditions $|\kappa_i|\leq 1/\tilde{r}$, and strict inequality is achieved at some point $y\in M$, then there are no eigenvalues. We apply these results to minimal graphic and multigraphic hypersurfaces.Comment: 16 pages. v2. Final version: minor revisions, we add Proposition 3.2. Accepted for publication in the Annali di Matematica Pura ed Applicata, on the 05/03/201

Down syndrome critical region protein 5 regulates membrane localization of Wnt receptors, Dishevelled stability and convergent extension in vertebrate embryos

The Glypican family of heparan sulfate proteoglycans regulates Wnt signaling and convergent extension (CE) in vertebrate embryos. They are predicted to be glycosylphosphatidylinositol (GPI)-tethered membrane-bound proteins, but there is no functional evidence of their regulation by the GPI synthesis complex. Down syndrome critical region protein 5 (Dscr5, also known as Pigp) is a component of the GPI-N-acetylglucosaminyltransferase (GPI-GnT) complex, and is associated with specific features of Down syndrome. Here we report that Dscr5 regulates CE movements through the non-canonical Wnt pathway. Both dscr5 overexpression and knockdown impaired convergence and extension movements. Dscr5 functionally interacted with Knypek/Glypican 4 and was required for its localization at the cell surface. Knockdown of dscr5 disrupted Knypek membrane localization and caused an enhanced Frizzled 7 receptor endocytosis in a Caveolin-dependent manner. Furthermore, dscr5 knockdown promoted specific Dishevelled degradation by the ubiquitin-proteosome pathway. These results reveal a functional link between Knypek/Glypican 4 and the GPI synthesis complex in the non-canonical Wnt pathway, and provide the new mechanistic insight that Dscr5 regulates CE in vertebrate embryos by anchoring different Wnt receptors at the cell surface and maintaining Dishevelled stability

Magnetic switching in granular FePt layers promoted by near-field laser enhancement

Light-matter interaction at the nanoscale in magnetic materials is a topic of intense research in view of potential applications in next-generation high-density magnetic recording. Laser-assisted switching provides a pathway for overcoming the material constraints of high-anisotropy and high-packing density media, though much about the dynamics of the switching process remains unexplored. We use ultrafast small-angle x-ray scattering at an x-ray free-electron laser to probe the magnetic switching dynamics of FePt nanoparticles embedded in a carbon matrix following excitation by an optical femtosecond laser pulse. We observe that the combination of laser excitation and applied static magnetic field, one order of magnitude smaller than the coercive field, can overcome the magnetic anisotropy barrier between "up" and "down" magnetization, enabling magnetization switching. This magnetic switching is found to be inhomogeneous throughout the material, with some individual FePt nanoparticles neither switching nor demagnetizing. The origin of this behavior is identified as the near-field modification of the incident laser radiation around FePt nanoparticles. The fraction of not-switching nanoparticles is influenced by the heat flow between FePt and a heat-sink layer

The H\"older-Poincar\'e Duality for Lq,pL_{q,p}-cohomology

We prove the following version of Poincare duality for reduced $L_{q,p}$-cohomology: For any $1<q,p<\infty$, the $L_{q,p}$-cohomology of a Riemannian manifold is in duality with the interior $L_{p',q'}-cohomology for$1/p+1/p'=1$,$1/q+1/q'=1$.Comment: 21 page