Discrete constant mean curvature nets in space forms: Steiner's formula and Christoffel duality

We show that the discrete principal nets in quadrics of constant curvature that have constant mixed area mean curvature can be characterized by the existence of a K\"onigs dual in a concentric quadric.Comment: 12 pages, 10 figures, pdfLaTeX (plain pdfTeX source included as bak file

Dynamic visualization of membrane-inserted fraction of pHluorin-tagged channels using repetitive acidification technique.

Background Changes in neuronal excitability, synaptic efficacy and generally in cell signaling often result from insertion of key molecules into plasma membrane (PM). Many of the techniques used for monitoring PM insertion lack either spatial or temporal resolution. Results We improved the imaging method based on time-lapse total internal reflection fluorescence (TIRF) microscopy and pHluorin tagging by supplementing it with a repetitive extracellular acidification protocol. We illustrate the applicability of this method by showing that brief activation of NMDA receptors ("chemical LTP") in cultured hippocampal neurons induced a persistent PM insertion of glutamate receptors containing the pHluorin-tagged GluR-A(flip) subunits. Conclusion The repetitive acidification technique provides a more accurate way of monitoring the PM-inserted fraction of fluorescently tagged molecules and offers a good temporal and spatial resolution

Kv4.2 potassium channels segregate to extrasynaptic domains and influence intrasynaptic NMDA receptor NR2B subunit expression

Neurons of the intercalated cell clusters (ITCs) represent an important relay site for information flow within amygdala nuclei. These neurons receive mainly glutamatergic inputs from the basolateral amygdala at their dendritic domains and provide feed-forward inhibition to the central nucleus. Voltage-gated potassium channels type-4.2 (Kv4.2) are main players in dendritic signal processing and integration providing a key component of the A currents. In this study, the subcellular localization and distribution of the Kv4.2 was studied in ITC neurons by means of light- and electron microscopy, and compared to other types of central principal neurons. Several ultrastructural immunolocalization techniques were applied including pre-embedding techniques and, most importantly, SDS-digested freeze-fracture replica labeling. We found Kv4.2 densely expressed in somato-dendritic domains of ITC neurons where they show a differential distribution pattern as revealed by nearest neighbor analysis. Comparing ITC neurons with hippocampal pyramidal and cerebellar granule cells, a cell type- and domain-dependent organization in Kv4.2 distribution was observed. Kv4.2 subunits were localized to extrasynaptic sites where they were found to influence intrasynaptic NMDA receptor subunit expression. In samples of Kv4.2 knockout mice, the frequency of NR1-positive synapses containing the NR2B subunit was significantly increased. This indicates a strong, yet indirect effect of Kv4.2 on the synaptic content of NMDA receptor subtypes, and a likely role in synaptic plasticity at ITC neurons. © 2012 The Author(s)

Loop Groups and Discrete KdV Equations

A study is presented of fully discretized lattice equations associated with the KdV hierarchy. Loop group methods give a systematic way of constructing discretizations of the equations in the hierarchy. The lattice KdV system of Nijhoff et al. arises from the lowest order discretization of the trivial, lowest order equation in the hierarchy, b_t=b_x. Two new discretizations are also given, the lowest order discretization of the first nontrivial equation in the hierarchy, and a "second order" discretization of b_t=b_x. The former, which is given the name "full lattice KdV" has the (potential) KdV equation as a standard continuum limit. For each discretization a Backlund transformation is given and soliton content analyzed. The full lattice KdV system has, like KdV itself, solitons of all speeds, whereas both other discretizations studied have a limited range of speeds, being discretizations of an equation with solutions only of a fixed speed.Comment: LaTeX, 23 pages, 1 figur

The Role of the IMF in Future Sovereign Debt Restructurings: Report of the Annenberg House Expert Group

A meeting of international finance and insolvency experts was held on November 2, 2013 at the Annenberg House in Santa Monica, California. The meeting was co-hosted by the USC Law School and the Annenberg Retreat at Sunnylands. The goal was to solicit the views of experts on the implications of the IMF’s April 26, 2013 paper captioned “Sovereign Debt Restructuring -- Recent Developments and Implications for the Fund’s Legal and Policy Framework”. The April 26 paper may signal a shift in IMF policies in the area of sovereign debt workouts. Although the Expert Group discussed a number of the ideas contained in the April 26 paper, attention focused on paragraph 32 of that paper. That paragraph states in relevant part: “There may be a case for exploring additional ways to limit the risk that Fund resources will simply be used to bail out private creditors. For example, a presumption could be established that some form of a creditor bail-in measure would be implemented as a condition for Fund lending in cases where, although no clear-cut determination has been made that the debt is unsustainable, the member has lost market access and prospects for regaining market access are uncertain.” This Report summarizes the consensus views of the Expert Group on the practical implications of the suggestions contained in paragraph 32 of the April 26 paper

Generalized isothermic lattices

We study multidimensional quadrilateral lattices satisfying simultaneously two integrable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Moebius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constraint imposed on the (complex) cross-ratio of the circular lattice. We derive the analogous condition for our generalized isthermic lattices using Steiner's projective structure of conics and we present basic geometric constructions which encode integrability of the lattice. In particular, we introduce the Darboux transformation of the generalized isothermic lattice and we derive the corresponding Bianchi permutability principle. Finally, we study two dimensional generalized isothermic lattices, in particular geometry of their initial boundary value problem.Comment: 19 pages, 11 figures; v2. some typos corrected; v3. new references added, higlighted similarities and differences with recent papers on the subjec

The PT-symmetric brachistochrone problem, Lorentz boosts and non-unitary operator equivalence classes

The PT-symmetric (PTS) quantum brachistochrone problem is reanalyzed as quantum system consisting of a non-Hermitian PTS component and a purely Hermitian component simultaneously. Interpreting this specific setup as subsystem of a larger Hermitian system, we find non-unitary operator equivalence classes (conjugacy classes) as natural ingredient which contain at least one Dirac-Hermitian representative. With the help of a geometric analysis the compatibility of the vanishing passage time solution of a PTS brachistochrone with the Anandan-Aharonov lower bound for passage times of Hermitian brachistochrones is demonstrated.Comment: 12 pages, 2 figures, strongly extended versio

An orthogonal biocatalytic approach for the safe generation and use of HCN in a multistep continuous preparation of chiral O-acetylcyanohydrins

An enantioselective preparation of O-acetylcyanohydrins has been accomplished by a three-step telescoped continuous process. The modular components enabled accurate control of two sequential biotransformations, safe handling of an in situ generated hazardous gas, and in-line stabilization of products. This method proved to be advantageous over the batch protocols in terms of reaction time (40 vs 345 min) and ease of operation, opening up access to reactions which have often been neglected due to safety concerns.We gratefully acknowledge the Deutsche Forschungsgemeinschaft (DFG) within the research training group GRK 1166 “Biocatalysis in non-conventional media (BioNoCo)”, and the EPSRC (Award Nos. EP/K009494/1 and EP/K039520/1)This is the final version of the article. It first appeared from Georg Thieme Verlag KG via http://dx.doi.org/10.1055/s-0035-156064