2-D R-matrix propagation: A large scale electron scattering simulation dominated by the multiplication of dynamically changing matrices

We examine the computational aspects of propagating a global R-matrix, R, across sub-regions in a 2-D plane. This problem originates in the large scale simulation of electron collisions with atoms and ions at intermediate energies. The propagation is dominated by matrix multiplications which are complicated because of the dynamic nature of R, which changes the designations of its rows and columns and grows in size as the propagation proceeds. The use of PBLAS to solve this problem on distributed memory HPC machines is the main focus of the paper.

Quadratic Forms on Complex Random Matrices and Multiple-Antenna Systems

This research published in the foremost international journal in information theory and shows interplay between complex random matrix and multiantenna information theory. Dr T. Ratnarajah is leader in this area of research and his work has been contributed in the development of graduate curricula (course reader) in Massachusetts Institute of Technology (MIT), USA, By Professor Alan Edelman. The course name is "The Mathematics and Applications of Random Matrices", see http://web.mit.edu/18.338/www/projects.html

Ionic liquid-reconstituted cellulose composites as solid support matrices for biocatalyst immobilization

Preparation of cellulose-polyamine composite films and beads, which provide high loading of primary amines on the surface allowing direct one-step bioconjugation of active species, is reported using an ionic liquid (IL) dissolution and regeneration process. Films and bead architectures were prepared and used as immobilization supports for laccase as a model system demonstrating the applicability of this approach. Performance of these materials, compared to commercially available products, has been assessed using millimeter-sized beads of the composites and the lipase-catalyzed transesterification of ethyl butyrate.

Comparison of porcine urine and bile as matrices to screen for the residues of two sulfonamides using a semi-automated enzyme immunoassay.

Porcine urine enzyme immunoassays for sulfamethazine and sulfadiazine have previously been employed as screening tests to predict the concentrations of the drugs in the corresponding tissues (kidneys), If a urine was found positive (> 800 ng ml(-1)) the corresponding kidney was then analysed by an enzyme immunoassay and, if found positive, a confirmatory analysis by HPLC was performed. Urine was chosen as the screening matrix since sulfonamides are mainly eliminated through this body fluid, However, after obtaining a number of false positive predictions, an investigation was carried out to assess the possibility of using an alternative body fluid which would act as a superior indicator of the presence of sulfonamides in porcine kidney, An initial study indicated that serum, plasma and bile could all be used as screening matrices. From these, bile was chosen as the preferred sample matrix and an extensive study followed to compare the efficiencies of sulfonamide positive bile and urine at predicting sulphonamide positive kidneys, Bile was found to be 17 times more efficient than urine at predicting a sulfamethazine positive kidney and 11 times more efficient at predicting a sulfadiazine positive kidney, With this enhanced performance of the initial screening test, the need for the costly and time consuming kidney enzyme immunoassay, prior to HPLC analysis, was eliminated

Distribution of the Demmel Condition Number of Wishart Matrices

This paper studies the Demmel condition number of Wishart matrices, a quantity which has numerous applications to wireless communications, such as adaptive switching between beamforming and diversity coding, link adaptation, and spectrum sensing. For complex Wishart matrices, we give an exact analytical expression for the probability density function (p.d.f.) of the Demmel condition number, and also derive simplified expressions for the high tail regime. These results indicate that the condition of complex Wishart matrices is dominantly decided by the difference between the matrix dimension and degree of freedom (DoF), i.e., the probability of drawing a highly ill conditioned matrix decreases considerably when the difference between the matrix dimension and DoF increases. We further investigate real Wishart matrices, and derive new expressions for the p.d.f. of the smallest eigenvalue, when the difference between the matrix dimension and DoF is odd. Based on these results, we succeed to obtain an exact p.d.f. expression for the Demmel condition number, and simplified expressions for the high tail regime.

On the Condition Number Distribution of Complex Wishart Matrices

This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multiple-input multipleoutput (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and non-central Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closed-form expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semi-correlated Rayleigh fading and Ricean fading. © 2010 IEEE.

In Vitro Release from Reverse Poloxamine/alpha-Cyclodextrin Matrices: Modelling and Comparison of Dissolution Profiles

Gels obtained by complexation of octablock star polyethylene oxide/polypropylene oxide copolymers (Tetronic 90R4) with -cyclodextrin (-CD) were evaluated as matrices for drug release. Both molecules are biocompatible so they can be potentially applied to drug delivery systems. Two different types of matrices of Tetronic 90R4 and -CD were evaluated: gels and tablets. These gels are capable to gelifying in situ and show sustained erosion kinetics in aqueous media. Tablets were prepared by freeze-drying and comprising the gels. Using these two different matrices, the release of two model molecules, L-tryptophan (Trp), and a protein, bovine serum albumin (BSA), was evaluated. The release profiles of these molecules from gels and tablets prove that they are suitable for sustained delivery. Mathematical models were applied to the release curves from tablets to elucidate the drug delivery mechanism. Good correlations were found for the fittings of the release curves to different equations. The results point that the release of Trp from different tablets is always governed by Fickian diffusion, whereas the release of BSA is governed by a combination of diffusion and tablet erosion. 

Ionic liquid reconstituted cellulose composites as solid support matrices with good transparency for biocatalytic reaction.

Disclosed are composites comprising regenerated cellulose, a first active substance, a second active substance, and a linker. Thus, microcryst. cellulose was dissolved in 1-butyl-3-methylimidazolium chloride using microwave pulse heating at 120-150°, cooled to 60° to form a super-cooled liq., 20% (based on cellulose) poly(L-lysine hydrobromide) was added therein, homogenized, cast onto a glass plate, the resulting film soaked in water for at least 24 h to leach residual from the film to give a reconstituted cellulose film, showing good transparency. [on SciFinder(R)]

An R -matrix with pseudo-states calculation of electron-impact excitation in C 2 +

We have performed an R-matrix with pseudo-states (RMPS) calculation of electron-impact excitation in C2+.Collision strengths and effective collision strengths were determined for excitation between the lowest 24 terms, including all those arising from the 2s3l and 2s4l configurations. In the RMPS calculation, 238 terms (90 spectroscopic and 148 pseudo-state) were employed in the close-coupling (CC) expansion of the target. In order to investigate the significance of coupling to the target continuum and highly excited bound states, we compare the RMPS results with those from an R-matrix calculation that incorporated all 238 terms in the configuration- interaction expansion, but only the lowest 44 spectroscopic terms in the CC expansion. We also compare our effective collision strengths with those from an earlier 12-state R-matrix calculation (Berrington et al 1989 J. Phys. B: At.Mol. Opt. Phys. 22 665). The RMPS calculation was extremely large, involving (N +1)-electron Hamiltonian matrices of dimension up to 36 085, and required the use of our recently completed suite of parallel R-matrix programs. The full set of effective collision strengths fromourRMPS calculation is available at theOakRidgeNationalLaboratoryControlledFusion Atomic Data Center web site. 1.