Twisted quantum affine superalgebra Uq[gl(m|n)(2)] and new Uq[osp(m|n)] invariant R-matrices

The minimal irreducible representations of U-q[gl(m|n)], i.e. those irreducible representations that are also irreducible under U-q[osp(m|n)] are investigated and shown to be affinizable to give irreducible representations of the twisted quantum affine superalgebra U-q[gl(m|n)((2))]. The U-q[osp(m|n)] invariant R-matrices corresponding to the tensor product of any two minimal representations are constructed, thus extending our twisted tensor product graph method to the supersymmetric case. These give new solutions to the spectral-dependent graded Yang-Baxter equation arising from U-q[gl(m|n)((2))], which exhibit novel features not previously seen in the untwisted or non-super cases.

Mesoionic pyridopyrimidinylium and pyridooxazinylium olates and non-mesoionic pyridopyrimidinones. Structures in the solid state, solution, and matrices

X-Ray crystal structures, C-13 NMR spectra and theoretical calculations (B3LYP/6-31G*) are reported for the mesoionic (zwitterionic) pyridopyrimidinylium- and pyridooxazinyliumolates 2a, 3a and 5a,b as well as the enol ether 11b and the enamine 11c. The 1-NH compounds like 1a, 2a and 3a exist in the mesoionic form in the crystal and in solution, but the OH tautomers such as 1b and 2b dominate in the gas phase as revealed by the Ar matrix IR spectra in conjunction with DFT calculations. All data indicate that the mesoionic compounds can be regarded as intramolecular pyridine-ketene zwitterions (cf. 16 --> 17) with a high degree of positive charge on the pyridinium nitrogen, a long pyridinium N-CO bond (ca. 1.44-1.49 Angstrom), and normal C=O double bonds (ca. 1.22 Angstrom). All mesoionic compounds exhibit a pronounced tilting of the olate C=O groups (the C=O groups formally derived from a ketene) towards the pyridinium nitrogen, giving NCO angles of 110-118 degrees. Calculations reveal a hydrogen bond with 6-CH, analogous to what is found in ketene-pyridine zwitterions and the C3O2-pyridine complex. The 2-OH tautomers of type 1b, 2b, and 11 also show a high degree of zwitterionic character as indicated by the canonical structures 11 12.

Unitary R-matrices for topological quantum computing

The main problem with current approaches to quantum computing is the difficulty of establishing and maintaining entanglement. A Topological Quantum Computer (TQC) aims to overcome this by using different physical processes that are topological in nature and which are less susceptible to disturbance by the environment. In a (2+1)-dimensional system, pseudoparticles called anyons have statistics that fall somewhere between bosons and fermions. The exchange of two anyons, an effect called braiding from knot theory, can occur in two different ways. The quantum states corresponding to the two elementary braids constitute a two-state system allowing the definition of a computational basis. Quantum gates can be built up from patterns of braids and for quantum computing it is essential that the operator describing the braiding-the R-matrix-be described by a unitary operator. The physics of anyonic systems is governed by quantum groups, in particular the quasi-triangular Hopf algebras obtained from finite groups by the application of the Drinfeld quantum double construction. Their representation theory has been described in detail by Gould and Tsohantjis, and in this review article we relate the work of Gould to TQC schemes, particularly that of Kauffman.

Twisted quantum affine superalgebra U-q[sl(2/2)((2))], U-q[osp(2/2)] invariant R-matrices and a new integrable electronic model

We describe the twisted affine superalgebra sl(2\2)((2)) and its quantized version U-q[sl(2\2)((2))]. We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point sub superalgebra U-q[osp(2\2)]. We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two U-q[osp(2\2)] invariant R-matrices: one of them corresponds to U-q [sl(2\2)(2)] and the other to U-q [osp(2\2)((1))]. Using the R-matrix for U-q[sl(2\2)((2))], we construct a new U-q[osp(2\2)] invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger sl(2\2) symmetry.

Reorganization of structural proteins in vascular smooth muscle cells grown in collagen gel and basement membrane matrices (Matrigel): A comparison with their in situ counterparts

When smooth muscle cells are enzyme-dispersed from tissues they lose their original filament architecture and extracellular matrix surrounds. They then reorganize their structural proteins to accommodate a 2-D growth environment when seeded onto culture dishes. The aim of the present study was to determine the expression and reorganization of the structural proteins in rabbit aortic smooth muscle cells seeded into 3-D collagen gel and Matrigel (a basement membrane matrix). It was shown that smooth muscle cells seeded in both gels gradually reorganize their structural proteins into an architecture similar to that of their in vivo counterparts. At the same time, a gradual decrease in levels of smooth muscle-specific contractile proteins (mainly smooth muscle myosin heavy chain-2) and an increase in p-nonmuscle actin occur, independent of both cell growth and extracellular matrix components. Thus, smooth muscle cells in 3-D extracellular matrix culture and in vivo have a similar filament architecture in which the contractile proteins such as actin, myosin, and alpha -actinin are organized into longitudinally arranged myofibrils and the vimentin-containing intermediate filaments form a meshed cytoskeletal network, However, the myofibrils reorganized in vitro contain less smooth muscle-specific and more nonmuscle contractile proteins. (C) 2001 Academic Press.

The design of hazard risk assessment matrices for ranking occupational health risks and their application in mining and minerals processing

Two hazard risk assessment matrices for the ranking of occupational health risks are described. The qualitative matrix uses qualitative measures of probability and consequence to determine risk assessment codes for hazard-disease combinations. A walk-through survey of an underground metalliferous mine and concentrator is used to demonstrate how the qualitative matrix can be applied to determine priorities for the control of occupational health hazards. The semi-quantitative matrix uses attributable risk as a quantitative measure of probability and uses qualitative measures of consequence. A practical application of this matrix is the determination of occupational health priorities using existing epidemiological studies. Calculated attributable risks from epidemiological studies of hazard-disease combinations in mining and minerals processing are used as examples. These historic response data do not reflect the risks associated with current exposures. A method using current exposure data, known exposure-response relationships and the semi-quantitative matrix is proposed for more accurate and current risk rankings.

Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (0(m)vertical bar alpha(n)) representations of U-q[gl(m vertical bar n)]

We detail the automatic construction of R matrices corresponding to (the tensor products of) the (O-m\alpha(n)) families of highest-weight representations of the quantum superalgebras Uq[gl(m\n)]. These representations are irreducible, contain a free complex parameter a, and are 2(mn)-dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a total of 2(4mn) components, each of which is in general an algebraic expression in the two complex variables q and a. Although the constructions are straightforward, we describe them in full here, to fill a perceived gap in the literature. As the algorithms are generally impracticable for manual calculation, we have implemented the entire process in MATHEMATICA; illustrating our results with U-q [gl(3\1)]. (C) 2002 Published by Elsevier Science B.V.

R-matrices and the tensor product graph method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

Relationship between flocculation of activated sludge and composition of extracellular polymeric substances

Activated sludge floes are a flocculated mass of microorganisms, extracellular polymeric substances (EPS) and adsorbed organic and inorganic material. The structure of the floes is very heterogeneous and floes with very different properties and morphologies may occur, depending on the conditions in the activated sludge treatment plant and wastewater composition. Present thinking suggests that cations, such as calcium, create cationic bridges with EPS excreted by the bacteria and thereby hold the various floe constituents together. However, due to the complex and heterogeneous nature of activated sludge, the mechanisms have neither been thoroughly investigated nor successfully quantified. A better understanding and description of the biological flocculation process is necessary in order to establish more efficient operational strategies. The main aim of this study was to get a comprehensive and unique insight into the floe properties of activated sludge and to assess the relative impact of chemical and physical parameters. A variety of sludges from full scale treatment plants with different settling properties were characterised. The interrelationships between floe parameters such as composition of EPS, surface properties and floe structure, and their effect on the flocculation and separation properties were assessed. The results indicate that the EPS, both in terms of quantity and quality, are very important for the floe properties of the activated sludge. However, presence of filaments may alter the physical properties of the floes considerably. The EPS showed positive correlations to sludge volume index (SVI) if only sludges with low or moderate numbers of filaments were included. The surface properties were more affected by the composition of the EPS than by the number of filaments. The EPS showed positive correlation to negative surface charge and a negative correlation to relative hydrophobicity and flocculation ability. The negative correlation between flocculation ability and amount of EPS was surprising. The shear sensitivity, measured as degree of erosion of floes when subjected to shear, was more affected by floe size and number of filaments than amount of EPS.

Thermal characterization of polyester-melamine coating matrices prepared under nonisothermal conditions

Thermal analysis methods (differential scanning calorimetry, thermogravimetric analysis, and dynamic mechanical thermal analysis) were used to characterize the nature of polyester-melamine coating matrices prepared under nonisothermal, high-temperature, rapid-cure conditions. The results were interpreted in terms of the formation of two interpenetrating networks with different glass-transition temperatures (a cocondensed polyester-melamine network and a self-condensed melamine-melamine network), a phenomenon not generally seen in chemically similar, isothermally cured matrices. The self-condensed network manifested at high melamine levels, but the relative concentrations of the two networks were critically dependent on the cure conditions. The optimal cure (defined in terms of the attainment of a peak metal temperature) was achieved at different oven temperatures and different oven dwell times, and so the actual energy absorbed varied over a wide range. Careful control of the energy absorption, by the selection of appropriate cure conditions, controlled the relative concentrations of the two networks and, therefore, the flexibility and hardness of the resultant coatings. (C) 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Cbem 41: 1603-1621, 2003.

Wurst: a protein threading server with a structural scoring function, sequence profiles and optimized substitution matrices

Wurst is a protein threading program with an emphasis on high quality sequence to structure alignments (http://www.zbh.uni-hamburg.de/wurst). Submitted sequences are aligned to each of about 3000 templates with a conventional dynamic programming algorithm, but using a score function with sophisticated structure and sequence terms. The structure terms are a log-odds probability of sequence to structure fragment compatibility, obtained from a Bayesian classification procedure. A simplex optimization was used to optimize the sequence-based terms for the goal of alignment and model quality and to balance the sequence and structural contributions against each other. Both sequence and structural terms operate with sequence profiles.

Scaffolds, stem cells, and tissue engineering: A potent combination!

Stem cells, either from embryonic or adult sources, have demonstrated the potential to differentiate into a wide range of tissues depending on culture conditions. This makes them prime candidates for use in tissue engineering applications. Current technology allows us to process biocompatible and biodegradable polymers into three-dimensional (3D) configurations, either as solid porous scaffolds or hydrogels, with controlled macro and/or micro spatial geometry and surface chemistry. Such control provides us with the ability to present highly controlled microenvironments to a chosen cell type. However, the precise microenvironments required for optimal expansion and/or differentiation of stem cells are only now being elucidated, and hence the controlled use of stem cells in tissue engineering remains a very young field. We present here a brief review of the current literature detailing interactions between stem cells and 3D scaffolds of varying morphology and chemical properties, concluding with remaining challenges for those interested in tissue engineering using tailored scaffolds and stem cells.