In this paper we describe uniied formulas for unitary and hyperbolic reeections and rotations, and show how these uniied transformations can be used to compute a Hermitian triangular decomposition ^ R H D ^ R of a strongly nonsingular indeenite matrix ^ A given in the form ^ The uniication is achieved by the introduction of signature matrices which determine whether the applicable transformatio...

Standard formulation is unable to distinguish between the (+ + +−) and (−−−+) spacetime metric signatures. However, the Clifford algebras associated with each are inequivalent, R(4) in the first case (real 4 by 4 matrices), H(2) in the latter (quaternionic 2 by 2). Multivector reformulations of Dirac theory by various authors look quite inequivalent pending the algebra assumed. It is not clear ...

For genomic applications, signature-finding algorithms identify over-represented signatures (words) in collections of DNA sequences. The results can be presented as a specific sequence of bases, a consensus sequence showing possible combination of bases, or a matrix of weighted possibilities at each position. These results are often compared to a biological set of binding sites (i.e., known fun...

the present study was undertaken to investigate the role of banana extract (be) on synchronous plantlet formation from seeds of dendrobium lituiflorum lindl. the seedlings formed on modified knudson c (kc) medium supplemented with 20% (v/v) be had significantly high fresh and dry weights. morphologically uniform plantlets with elongated leaves and well developed roots were formed on kc medium w...

When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...

Graphlet analysis is part of network theory that does not depend on the choice of the network null model and can provide comprehensive description of the local network structure. Here, we propose a novel method for graphlet-based analysis of directed networks by computing first the signature vector for every vertex in the network and then the graphlet correlation matrix of the network. This ana...

Background. Interpretation of microarray data remains challenging because biological meaning should be extracted from enormous numeric matrices and be presented explicitly. Moreover, huge public repositories of microarray dataset are ready to be exploited for comparative analysis. This study aimed to provide a platform where essential implication of a microarray experiment could be visually exp...

Abstract We use the geometric mean to parametrize metrics in Hassan–Rosen ghost-free bimetric theory and pose initial-value problem. The of two positive definite symmetric matrices is a well-established mathematical notion which can be under certain conditions extended quadratic forms having Lorentzian signature, say g f . In such case, null cone metric h middle cones appearing as average space...