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

The conjugacy problem for two-by-two matrices over polynomial rings

We give an effective solution of the conjugacy problem for two-by-two matrices over the polynomial ring in one variable over a finite field.

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.

Characterizing multipartite symmetric Dicke states under the effects of noise

We study genuine multipartite entanglement (GME) in a system of n qubits prepared in symmetric Dicke states and subjected to the influences of noise. We provide general, setup-independent expressions for experimentally favorable tools such as fidelity- and collective spin-based entanglement witnesses, as well as entangled-class discriminators and multi-point correlation functions. Besides highlighting the effects of the environment on large qubit registers, we also discuss strategies for the robust detection of GME. Our work provides techniques and results for the experimental communities interested in investigating and characterizing multipartite entangled states by introducing realistic milestones for setup design and associated predictions.

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.