Crystals from categorified quantum groups

We study the crystal structure on categories of graded modules over algebras which categorify the negative half of the quantum Kac–Moody algebra associated to a symmetrizable Cartan data. We identify this crystal with Kashiwara?s crystal for the corresponding negative half of the quantum Kac–Moody algebra. As a consequence, we show the simple graded modules for certain cyclotomic quotients carry the structure of highest weight crystals, and hence compute the rank of the corresponding Grothendieck group.     

Open sets with the Runge property in Banach spaces

We show that every pseudoconvex open subset of a Banach space with an unconditional Schauder basis has the F-valued Runge property for every Banach space F.     

Impact of insurance for operational risk: Is it worthwhile to insure or be insured for severe losses?

Under the Basel II standards, the Operational Risk (OpRisk) advanced measurement approach allows a provision for reduction of capital as a result of insurance mitigation of up to 20%. This paper studies different insurance policies in the context of capital reduction for a range of extreme loss models and insurance policy scenarios in a multi-period, multiple risk setting. A Loss Distributional Approach (LDA) for modeling of the annual loss process, involving homogeneous compound Poisson processes for the annual losses, with heavy-tailed severity models comprised of α-stable severities is considered. There has been little analysis of such models to date and it is believed insurance models will play more of a role in OpRisk mitigation and capital reduction in future. The first question of interest is when would it be equitable for a bank or financial institution to purchase insurance for heavy-tailed OpRisk losses under different insurance policy scenarios? The second question pertains to Solvency II and addresses quantification of insurer capital for such operational risk scenarios. Considering fundamental insurance policies available, in several two risk scenarios, we can provide both analytic results and extensive simulation studies of insurance mitigation for important basic policies, the intention being to address questions related to VaR reduction under Basel II, SCR under Solvency II and fair insurance premiums in OpRisk for different extreme loss scenarios. In the process we provide closed-form solutions for the distribution of loss processes and claims processes in an LDA structure as well as closed-form analytic solutions for the Expected Shortfall, SCR and MCR under Basel II and Solvency II. We also provide closed-form analytic solutions for the annual loss distribution of multiple risks including insurance mitigation.     

Partitioning of star branched polymers into pores at three chromatography conditions

The partitioning of star branched polymers into a slit pore at three different chromatography conditions, namely, size exclusion chromatography (SEC), liquid chromatography at the critical condition (LCCC), and liquid adsorption chromatography (LAC) have been investigated with lattice Monte Carlo simulations. Two different chain models are used: random walks (RW) that have no excluded volume interaction and self-avoiding walks (SAW) that have excluded volume interaction. The simulation data obtained for the two chain models are compared to illustrate the effect of excluded volume interactions on the partitioning of star branched polymers. The two most outstanding effects observed due to the introduction of excluded volume interactions are: (i) stars with a high number of arms can be excluded from the pore at condition corresponding to the LCCC of the linear polymers; (ii) the partition coefficient of stars in LAC mode is not dependent only on the total number of monomers on the chain. These effects illustrated by the current study should be taken into account when interpreting experimental chromatography data for branched polymers.     

Trinuclear Metal Clusters in Catalysis by Terpenoid Synthases

Terpenoid synthases are ubiquitous enzymes that catalyze the formation of structurally and stereochemically diverse isoprenoid natural products. Many isoprenoid coupling enzymes and terpenoid cyclases from bacteria, fungi, protists, plants, and animals share the class I terpenoid synthase fold. Despite generally low amino acid sequence identity among these examples, class I terpenoid synthases contain conserved metal binding motifs that coordinate to a trinuclear metal cluster. This cluster not only serves to bind and orient the flexible isoprenoid substrate in the precatalytic Michaelis complex, but it also triggers the departure of the diphosphate leaving group to generate a carbocation that initiates catalysis. Additional conserved hydrogen bond donors assist the metal cluster in this function. Crystal structure analysis reveals that the constellation of three metal ions required for terpenoid synthase catalysis is generally identical among all class I terpenoid synthases of known structure.     

Spectroscopic characterization of bionanoparticles originating from newly developed self-forming synthetic PEGylated lipids (QuSomes)

In this work, we have aimed to merge the advantages of nanotechnology and biophotonics in conjunction with vibrational spectroscopic techniques in order to understand the various aspects of new kinds of synthetic bionanoparticles originating from self-forming synthetic biopolymers known as polyethylene glycol (PEG)ylated lipids. In particular, two complementary molecular spectroscopic techniques based on thin-layered Fourier transform infrared and confocal laser tweezers. Raman spectroscopy has been employed for the investigations of newly developed artificial PEGylated lipids trademarked as QuSomes. These novel types of synthetic lipids are composed of 1,2-dimyristoyl-rac-glycerol-3-dodecaethylene glycol (GDM-12), 1,2-dioleoyl-rac-glycerol-3-dodecaethylene glycol (GDO-12), and 1,2-distearoyl-rac-glycerol-3-triicosaethylene glycol (GDS-23). The lipid labeled GDM-12 has saturated 14 acyl chains whereas GDO-12 is characterized by monounsaturated 18 acyl chains, and GDS-23 is composed of saturated 18 acyl chains in their hydrophobic chain. Similarly, GDM-12 and GDO-12 contain 12 units, and GDS-23 contains 23 units of hydrophilic PEG head groups. In contrast to conventional phospholipids, this novel kind of lipid can form liposomes spontaneously upon hydration, without the input of external activation energy. In addition, fluorescence correlation spectroscopy has been utilized to measure the size distribution of such nanoparticles in suspension as well as scanning electron microscopy has been applied for the imaging purposes. Although such PEGylated lipids show a common spectral pattern, important differences in the spectra have been observed, enabling us to distinguish these different lipids on the basis of characteristic features calculated from the spectroscopic band component analysis. Finally, in this study, detailed spectroscopic results due to the vibrational band assignments and band component analysis corresponding to various functional groups for individual nanoparticles have been analyzed and discussed.     

Atomic-force-controlled capillary electrophoretic nanoprinting of proteins

The general nanoprinting and nanoinjection of proteins on non-conducting or conducting substrates with a high degree of control both in terms of positional and timing accuracy is an important goal that could impact diverse fields from biotechnology (protein chips) to molecular electronics and from fundamental studies in cell biology to nanophotonics. In this paper, we combine capillary electrophoresis (CE), a separation method with considerable control of protein movement, with the unparalleled positional accuracy of an atomic force microscope (AFM). This combination provides the ability to electrophoretically or electroosmotically correlate the timing of protein migration with AFM control of the protein deposition at a high concentration in defined locations and highly confined volumes estimated to be 2 al. Electrical control of bovine serum albumin printing on standard protein-spotting glass substrates is demonstrated. For this advance, fountain pen nanolithography (FPN) that uses cantilevered glass-tapered capillaries is amended with the placement of electrodes on the nanopipette itself. This results in imposed voltages that are three orders of magnitude less than what is normally used in capillary electrophoresis. The development of atomic-force-controlled capillary electrophoretic printing (ACCEP) has the potential for electrophoretic separation, with high resolution, both in time and in space. The large voltage drop at the tip of the tapered nanopipettes allows for significant increases in concentration of protein in the small printed volumes. All of these attributes combine to suggest that this methodology should have a significant impact in science and technology.      

Nanopore detection of 8-oxo-7,8-dihydro-2'-deoxyguanosine in immobilized single-stranded DNA via adduct formation to the DNA damage site

The ability to detect DNA damage within the context of the surrounding sequence is an important goal in medical diagnosis and therapies, but there are no satisfactory methods available to detect a damaged base while providing sequence information. One of the most common base lesions is 8-oxo-7,8-dihydroguanine, which occurs during oxidation of guanine. In the work presented here, we demonstrate the detection of a single oxidative damage site using ion channel nanopore methods employing α-hemolysin. Hydantoin lesions produced from further oxidation of 8-oxo-7,8-dihydroguanine, as well as spirocyclic adducts produced from covalently attaching a primary amine to the spiroiminodihydantoin lesion, were detected by tethering the damaged DNA to streptavidin via a biotin linkage and capturing the DNA inside an α-hemolysin ion channel. Spirocyclic adducts, in both homo- and heteropolymer background single-stranded DNA sequences, produced current blockage levels differing by almost 10% from those of native base current blockage levels. These preliminary studies show the applicability of ion channel recordings not only for DNA sequencing, which has recently received much attention, but also for detecting DNA damage, which will be an important component to any sequencing efforts.     

Iron acyl thiolato carbonyls: structural models for the active site of the [Fe]-hydrogenase (Hmd)

Phosphine-modified thioester derivatives are shown to serve as efficient precursors to phosphine-stabilized ferrous acyl thiolato carbonyls, which replicate key structural features of the active site of the hydrogenase Hmd. The reaction of Ph(2)PC(6)H(4)C(O)SPh and sources of Fe(0) generates both Fe(SPh)(Ph(2)PC(6)H(4)CO)(CO)(3) (1) and the diferrous diacyl Fe(2)(SPh)(2)(CO)(3)(Ph(2)PC(6)H(4)CO)(2), which carbonylates to give 1. For the extremely bulky arylthioester Ph(2)PC(6)H(4)C(O)SC(6)H(3)-2,6-(2,4,6-trimethylphenyl)(2), oxidative addition is arrested and the Fe(0) adduct of the phosphine is obtained. Complex 1 reacts with cyanide to give Et(4)N[Fe(SPh)(Ph(2)PC(6)H(4)CO)(CN)(CO)(2)] (Et(4)N[2]). (13)C and (31)P NMR spectra indicate that substitution is stereospecific and cis to P. The IR spectrum of [2](-) in ν(CN) and ν(CO) regions very closely matches that for Hmd(CN). XANES and EXAFS measurements also indicate close structural and electronic similarity of Et(4)N[2] to the active site of wild-type Hmd. Complex 1 also stereospecifically forms a derivative with TsCH(2)NC, but the adduct is more labile than Et(4)N[2]. Tricarbonyl 1 was found to reversibly protonate to give a thermally labile derivative, IR measurements of which indicate that the acyl and thiolate ligands are probably not protonated in Hmd.     

A Stream Function Approach to Optical Flow with Applications to Fluid Transport Dynamics

Optical flow is one of the classical problems in computer vision, but it has recently also been adapted to applications from other fields, such as fluid mechanics and dynamical systems. If the goal is to analyze the dynamics of system whose evolution is governed by a flow field that is the gradient of a potential function – which describes many flows in fluid dynamics – it is natural to approach the optical flow problem by reconstructing the potential function, also called the stream function, rather than reconstructing the components of the flow directly. This alternate approach allows one to impose scientific priors, via regularization, directly on the flow itself rather than on its components independently. We demonstrate the stream function formulation of optical flow and its application to reconstructing an oceanic fluid flow driven by satellite measurements. It is also shown how these flow fields can be used to analyze mixing and mass transport in the fluid system being imaged. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)