Quaternionic Kähler Detour Complexes and $${\mathcal{N} = 2}$$ Supersymmetric Black Holes

We study a class of supersymmetric spinning particle models derived from the radial quantization of stationary, spherically symmetric black holes of four dimensional \({{\mathcal N} = 2}\) supergravities. By virtue of the c-map, these spinning particles move in quaternionic Kähler manifolds. Their spinning degrees of freedom describe mini-superspace-reduced supergravity fermions. We quantize these models using BRST detour complex technology. The construction of a nilpotent BRST charge is achieved by using local (worldline) supersymmetry ghosts to generate special holonomy transformations. (An interesting byproduct of the construction is a novel Dirac operator on the superghost extended Hilbert space.) The resulting quantized models are gauge invariant field theories with fields equaling sections of special quaternionic vector bundles. They underly and generalize the quaternionic version of Dolbeault cohomology discovered by Baston. In fact, Baston’s complex is related to the BPS sector of the models we write down. Our results rely on a calculus of operators on quaternionic Kähler manifolds that follows from BRST machinery, and although directly motivated by black hole physics, can be broadly applied to any model relying on quaternionic geometry.     

Hermite polynomials on the plane

The space of bivariate generalised Hermite polynomials of degree n is invariant under rotations. We exploit this symmetry to construct an orthonormal basis for which consists of the rotations of a single polynomial through the angles , ℓ=0,...n. Thus we obtain an orthogonal expansion which retains as much of the symmetry of as is possible. Indeed we show that a continuous version of this orthogonal expansion exists.      

Phosphorylation-dependent protein kinase D activation

The novel mouse serine-threonine kinase protein kinase D (PKD) is activated in intact Swiss 3T3 cells stimulated by phorbol esters, cell permeant diacylglycerols, bryostatin, neuropeptides and growth factors via a phosphorylation-dependent mechanism requiring protein kinase C (PKC) activity. Structural comparison of the PKD catalytic domain with other kinases reveals a close similarity with MEK family kinases, which are activated upon phosphorylation of key serine and threonine residues in a region termed the activation loop. To study the regulation of PKD, we transfected mutant PKD cDNAs in which putative activation loop serine residues 744 and 748 were mutated to either alanine or glutamic acid into COS-7 cells. Replacement of serines 744 and 748 with alanine prevented activation of the overexpressed PKD form upon phorbol ester treatment of cells, whereas replacement with glutamic acid results in full constitutive activation. Single serine to glutamic acid replacement mutants were partially activated. In vivo 32P-labeling and two-dimensional phosphopeptide mapping of PKD and catalytically inactive PKD mutants at serine 744, 748 or at both residues revealed that phorbol ester-sensitive phosphopeptides could be selectively eliminated from patterns observed as a result of these mutations. Treatment of cells with the PKC inhibitor GFI also prevented the appearance of phosphopeptide spots occuring in response to phorbol ester stimulation. These results provide direct evidence that PKD becomes activated in vivo as a consequence of PKC-mediated phosphorylation of serines 744 and 748. These results support our view of PKD as an important clement in PKC signal transduction.     

Attachment of a single fluorescent label to peptides for determination by capillary zone electrophoresis.

Complicated electropherograms are produced in the separation of fluorescently labeled peptides. Incomplete labeling of epsilon-amino groups on lysine residues results in the production of 2n-1 reaction products, where n is the number of alpha and epsilon amino groups in the peptide. A single label is attached to the peptide by first taking the peptide through one cycle of the Edman degradation reaction. All epsilon-amino groups are converted to the phenyl thiocarbamyl and the cleavage step exposes one alpha-amino group at the N-terminus of the peptide; the fluorescent label is attached to the N-terminus.     

Multidimensional NMR cross-correlation relaxation study of carrot phloem and xylem. Part II: Thermal and high-pressure processing

The effects of thermal and high-pressure processing on the phloem and xylem tissue of carrots are investigated with a combination of optical fluorescence microscopy and two-dimensional nuclear magnetic resonance relaxometry. It is shown that precooking at 60 °C or rapid pressurization to 600 MPa prevents the cell-wall separation and that the combination of these two treatments may provide a commercially viable method for tissue texture preservation.     

The current state of public understanding of nanotechnology

The growing importance of nanotechnology in industry and society has not been accompanied by a widespread understanding of the subject among the general public. Simple questions to initially probe the smallest thing that people can see and can think of reveals a divide in the understanding of the general public. A survey of 1500 individuals ranging in age from 6 to 74 has revealed a lack of knowledge of nanotechnology and especially a lack of understanding of the context of nanotechnology in the world that is too small to see. Survey findings are corroborated by in-depth interviews with 400 adults in studies of nanoscience literacy commisioned by University of California, Berkeley and Cornell in 2002 and 2004, respectively. In general, with the exception of 14–28 year olds, over 60% of respondents say they have never heard of nano or nanotechnology. The results suggest that the general public, especially middle-school children, has no firm foundation to understand nanotechnology and likely will continue to be equally impressed by credible scientific information as well as pure fictional accounts of nanotechnology.     

On the construction of highly symmetric tight frames and complex polytopes

Many “highly symmetric” configurations of vectors in C^d${\mathbb{C}}^d$, such as the vertices of the platonic solids and the regular complex polytopes, are equal-norm tight frames by virtue of being the orbit of the irreducible unitary action of their symmetry group. For nonabelian groups there are uncountably many such tight frames up to unitary equivalence. The aim of this paper is to single out those orbits which are particularly nice, such as those which are the vertices of a complex polytope. This is done by defining a finite class of tight frames of n   vectors for C^d${\mathbb{C}}^d$ (n and d fixed) which we call the highly symmetric tight frames. We outline how these frames can be calculated from the representations of abstract groups using a computer algebra package. We give numerous examples, with a special emphasis on those obtained from the (Shephard–Todd) finite reflection groups. The interrelationships between these frames with complex polytopes, harmonic frames, equiangular tight frames, and Heisenberg frames (maximal sets of equiangular lines) are explored in detail.     

The role of mannitol in affecting the thermal transitions in carrot tissue

Dynamic mechanical thermal analysis (DMTA) and differential scanning calorimetry (DSC) were used to observe thermal events in osmotically manipulated carrot. A glass transition of the concentrated amorphous solution (CAS), recrystallisation of water and ice melting were shown in the tissue by DMTA. DSC showed the role of mannitol as a plasticiser in freeze-dried osmotically manipulated carrot tissue, lowering the cell wall rich and sugar rich phase glass transitions. This cautions against the use of mannitol as an osmoticum for texture measurement since a decrease in stiffness could be due to shift towards a more rubbery state or a reduction of turgor. Processing treatments of air-drying-rehydrating, freezing-thawing or heating-cooling without prior osmotic treatment, induced consistently lower stiffness of carrot tissue compared to that of fresh specimens. The order of stiffness decrease was: fresh>drying-rehydrating∼heating-cooling>freezing-thawing. When osmotically manipulated carrot tissue was processed, stiffness decreased in comparison with osmotically treated specimens alone for molarities less than isotonic. Stiffness could not be restored further to any process events after osmotic changes, demonstrating the irreversible effect of processing on stiffness and contrary to some earlier reports that a prior decrease in turgor would enable the mechanical properties to be recovered.